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By means of Riccati transformation technique and inequalities, the oscillation criteria for second order delay dynamic equations on time scales with mixed nonlinearities are studied. Two sufficient conditions are obtained for oscillation of this equation. The results in this paper extend and improve some known results for the corresponding equations with mixed nonlinearities.
In this paper, we study the existence and uniqueness of solutions for the nonlinear fractional differential equation initial value problem Dαu(t) = f(t, u(t)), t ∈ (0, T], t2-αu(t)|t=0 = b1, t2-αu'(t)|t=0 = b2, where 1 <; a <; 2 is a real number, Dα is the Riemann-Liouville fractional derivative. Using the monotone iterative method and the lower and upper solution method, some existence and...
In this paper, we study the existence of positive solutions for the singular nonlinear fractional differential equation boundary value problem D0+α u(t) + f(t,u(t)) = 0, 0 <; t <; 1, u(0) = u(1) = u'(0) = 0, where 2 <; α ≤ 3 is a real number, D0+α is the Riemann-Liouville fractional derivative, and f : (0,1] × [0, + ∞) → [0, + ∞) is continuous, limt→0+ f(t, ·) = + ∞ (i.e., f is singular at...
In this paper, we consider the discrete hybrid system with different initial times. By employing variational cone-valued Lyapunov-like functions, we get some comparison theorems and several φ0-stability criteria for discrete hybrid system with different initial values.
By means of Riccati transformation technique, we will establish some new oscillation criteria for the second-order nonlinear delay dynamic equation (p(t) (xΔ(t)y)Δ +q(t)f(x(t(t))) = 0 on a time scale T; here γ ≥ 1 is an odd positive integers with p and q real-valued positive functions defined on T. Our results improve and extend some results established by Saker [S. H. Saker, Oscillation criteria...
By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order delay dynamic equations. Our results in this paper not only extend the results given in Sahiner [?] but also unify the oscillation of the second order nonlinear delay differential equation and the second order nonlinear delay difference equation.
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