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Items from 1 to 20 out of 33 results

article

Existence and nonexistence results for a class of fourth‐order coupled singular boundary value problems arising in the theory of epitaxial growth

Amit K. Verma, Biswajit Pandit, Ravi P. Agarwal

Mathematical Methods in the Applied Sciences > 47 > 13 > 11147 - 11180

In this article, we propose novel coupled nonlinear singular boundary value problems arising in epitaxial growth theory. The coupled equations are nonlinear, non‐self‐adjoint, and singular and have no exact solutions. We derive some qualitative properties of the coupled solutions, which depend on the size of parameters that occur in the coupled system. To prove the existence of the coupled solutions,...

article

On implicit fractional q‐difference equations: Analysis and stability

Nadjet Laledj, Abdelkrim Salim, Jamal Eddine Lazreg, Saïd Abbas, more

Mathematical Methods in the Applied Sciences > 45 > 17 > 10775 - 10797

This paper deals with some existence and Ulam stability results for some classes of implicit fractional

q

‐difference equations with and without random effects in Banach spaces and Banach algebras. Our results are provided by applying the fixed point theory (Itoh's random fixed point theorem, the nonlinear alternative of Schaefer's type proved by Dhage, and an other Dhage's random fixed point...

article

Extremal solutions of measure differential equations

Giselle Antunes Monteiro, Antonín Slavík

Journal of Mathematical Analysis and Applications > 2016 > 444 > 1 > 568-597

We investigate the existence of the least and greatest solutions to measure differential equations, as well as the relation between the extremal solutions and lower or upper solutions. Along the way, we prove a fairly general local existence theorem and an analogue of Peano's uniqueness theorem for measure differential equations. Finally, we show that the general theory is applicable in the study...

article

Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses

Saïd Abbas, Mouffak Benchohra, Mohamed Abdalla Darwish

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 2016 > 36 > 2 > 155-179

In this paper, we use the upper and lower solutions method combined with a fixed point theorem for multivalued maps in Banach algebras due to Dhage for investigations of the existence of solutions of a class of discontinuous partial differential inclusions with not instantaneous impulses. Also, we study the existence of extremal solutions under Lipschitz, Carath´eodory and certain monotonicity conditions

article

Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions

Saïd Abbas, Eman Alaidarous, Wafaa Albarakati, Mouffak Benchohra

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 2015 > 35 > 2 > 105-122

In this paper we use the upper and lower solutions method combined with Schauder's fixed point theorem and a fixed point theorem for condensing multivalued maps due to Martelli to investigate the existence of solutions for some classes of partial Hadamard fractional integral equations and inclusions.

article

Existence of solutions to fourth-order differential equations with deviating arguments

Mostepha Naceri, Ravi P Agarwal, Erbil Çetin, El Haffaf Amir

Boundary Value Problems > 2015 > 2015 > 1 > 1-31

In this paper, we consider fourth-order differential equations on a half-line with deviating arguments of the form u ( 4 ) ( t ) + q ( t ) f ( t , [ u ( t ) ] , [ u ′ ( t ) ] , [ u ″ ( t ) ] , u ‴ ( t ) ) = 0 $u^{(4)}(t)+q(t)f(t,[u(t)],[u'(t)],[u''(t)],u'''(t))=0$ , 0 < t < + ∞ $0< t<{+\infty}$ , with the boundary conditions u ( 0 ) = A $u(0)=A$ , ...

article

Upper and lower solution method for nth-order BVPs on an infinite interval

Hairong Lian, Junfang Zhao, Ravi P Agarwal

Boundary Value Problems > 2014 > 2014 > 1 > 1-17

This work is devoted to the study of nth-order ordinary differential equations on a half-line with Sturm-Liouville boundary conditions. The existence results of a solution, and triple solutions, are established by employing a generalized version of the upper and lower solution method, the Schäuder fixed point theorem, and topological degree theory. In our problem the nonlinearity depends on derivatives,...

article

A result on three solutions theorem and its application to p-Laplacian systems with singular weights

Eun Kyoung Lee, Yong-Hoon Lee

Boundary Value Problems > 2012 > 2012 > 1 > 1-20

In this paper, we consider p-Laplacian systems with singular weights. Exploiting Amann type three solutions theorem for a singular system, we prove the existence, nonexistence, and multiplicity of positive solutions when nonlinear terms have a combined sublinear effect at ∞. MSC: 35J55, 34B18.

article

Traveling wave solutions in temporally discrete reaction‐diffusion systems with delays

J. Xia, Z. Yu

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für... > 91 > 10 > 809 - 823

An idea used by W. Li et al. (Nonlinearity 19, 1253–73, 2006) is extended to show existence of traveling wave solutions for a class of temporally discrete reaction‐diffusion systems with delays. The result is an generalization of an existing result for scalar equations to systems. As examples, the obtained abstract results will be applied to temporally discrete diffusion‐competition systems with delay...

chapter

Monotone Traveling Wave Solution for a Delayed Reaction-Diffusion Equations

Zhihao Ge

2010 International Workshop on Chaos-Fractal Theories and Applications > 69 - 71

2010 International Workshop on Chaos-Fractals Theories and Applications (IWCFTA 2010)

In the paper, we derive a delayed reaction-diffusion equations, which describes a multi-species Predator-prey system. By coupling the perturbation approach with the method of upper and lower solutions, we prove that the traveling wave fronts exist and appear monotone, which connect the zero solution with the positive steady state. Finally, we draw a conclusion to point out that the existence of traveling...

article

Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order

Saïd Abbas, Mouffak Benchohra

Nonlinear Analysis: Hybrid Systems > 2010 > 4 > 3 > 406-413

In this paper we investigate the existence of solutions for a class of initial value problems for impulsive partial hyperbolic differential equations involving the Caputo fractional derivative by using the lower and upper solutions method combined with Schauder’s fixed point theorem.

article

The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses

Saïd Abbas, Mouffak Benchohra

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 2010 > 30 > 1 > 141-161

In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems.

article

Block monotone iterative algorithms for variational inequalities with nonlinear operators

Ming-hui Ren, Jin-ping Zeng

Acta Mathematicae Applicatae Sinica, English Series > 2008 > 24 > 2 > 221-232

Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in...

article

Existence theorems for a class of nonlocal differential equations

Ronald Begg

Journal of Mathematical Analysis and Applications > 2006 > 322 > 2 > 1168-1187

A class of nonlocal second-order ordinary differential equations of the formy″(x)=f(x,y(x),(y○λ)(x),y′(x)) for continuous f and λ is studied. The equation is supplemented with none, one, or two Robin boundary conditions depending on whether the interval of interest I is finite, semi-infinite or infinite. The only other restriction on the function λ is that it maps I into itself. Sufficient conditions...

article

Nonhomogeneous boundary value problem for first-order impulsive differential equations with delay

Fengqin Zhang, Meili Li, Jurang Yan

Computers and Mathematics with Applications > 2006 > 51 > 6-7 > 927-936

The authors employ the method of upper and lower solution coupled with the monotone iterative technique to obtain results of existence and uniqueness for a nonhomogeneous boundary value problem of impulsive differential equations with delay.

article

Nonsmooth critical point theory on closed convex sets and nonlinear hemivariational inequalities

Sophia Th. Kyritsi, Nikolaos S. Papageorgiou

Nonlinear Analysis > 2005 > 61 > 3 > 373-403

In this paper we develop a critical point theory for nonsmooth locally Lipschitz functionals defined on a closed, convex set extending this way the work of Struwe (Variational Methods, Springer, Berlin, 1990). Through a deformation result, we obtain minimax principles producing critical points. Then we use the theory to obtain positive and negative solutions of nonlinear and semilinear hemivariational...

article

Mean value theorem for boundary value problems with given upper and lower solutions

S.K. Sen, H. Agarwal

Computers and Mathematics with Applications > 2005 > 49 > 9-10 > 1499-1514

An approach based on successive application of the mean value theorem or, equivalently, a successive linear interpolation that excludes extrapolation, is described for two-point boundary value problem (BVP) associated with nonlinear ordinary differential equations (ODEs). The approach is applied to solve numerically a two-point singular BVP associated with a second-order nonlinear ODE which is a mathematical...

article

The Method of Upper and Lower Solutions for a Lidstone Boundary Value Problem

Yanping Guo, Ying Gao

Czechoslovak Mathematical Journal > 2005 > 55 > 3 > 639-652

In this paper we develop the monotone method in the presence of upper and lower solutions for the 2nd order Lidstone boundary value problem $$\begin{array}{*{20}c} {u^{(2n)} (t) = f(t,\;u(t),\;u''(t),...,u^{(2(n - 1))} (t)),\quad 0 < t < 1,} \\ {u^{(2i)} (0) = u^{(2i)} (1) = 0,\quad 0 \leqslant i \leqslant n - 1,} \\ \end{array}$$ where f : [0, 1] × ℝⁿ → ℝ is continuous. We obtain sufficient...

article

Travelling wavefronts in delayed cooperative and diffusive systems with non-local effects

Huang Jianhua, Huang Lihong

Applied Mathematics-A Journal of Chinese Universities > 2005 > 20 > 3 > 363-375

In this paper, traveling wavefront solutions are established for two cooperative systems with time delay and non-local effects. The results are an extension of the existing results for delayed logistic scale equations and diffusive Nicholson equations with non-local effects to systems. The approach used is the upper-lower solution technique and Schauder fixed point Theorem developed by Ma (J Differential...

article

Existence of traveling wave fronts of delayed lattice differential equations

Jianhua Huang, Gang Lu, Xingfu Zou

Journal of Mathematical Analysis and Applications > 2004 > 298 > 2 > 538-558

Existence of traveling wave fronts for delayed lattice differential equations is established by Schauder fixed point theorem. The main result is applied to a delayed and discretely diffusive model for the population of Daphnia magna.

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Search results

Existence and nonexistence results for a class of fourth‐order coupled singular boundary value problems arising in the theory of epitaxial growth

On implicit fractional q‐difference equations: Analysis and stability

Extremal solutions of measure differential equations

Upper and lower solutions method for partial discontinuous fractional differential inclusions with not instantaneous impulses

Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions

Existence of solutions to fourth-order differential equations with deviating arguments

Upper and lower solution method for nth-order BVPs on an infinite interval

A result on three solutions theorem and its application to p-Laplacian systems with singular weights

Traveling wave solutions in temporally discrete reaction‐diffusion systems with delays

Monotone Traveling Wave Solution for a Delayed Reaction-Diffusion Equations

Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order

The method of upper and lower solutions for partial hyperbolic fractional order differential inclusions with impulses

Block monotone iterative algorithms for variational inequalities with nonlinear operators

Existence theorems for a class of nonlocal differential equations

Nonhomogeneous boundary value problem for first-order impulsive differential equations with delay

Nonsmooth critical point theory on closed convex sets and nonlinear hemivariational inequalities

Mean value theorem for boundary value problems with given upper and lower solutions

The Method of Upper and Lower Solutions for a Lidstone Boundary Value Problem

Travelling wavefronts in delayed cooperative and diffusive systems with non-local effects

Existence of traveling wave fronts of delayed lattice differential equations

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