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In this paper we consider sharp conditions on ω and f for the existence of C1[0,1] positive solutions to a second-order singular nonlocal problem u″(t)+ω(t)f(t,u(t))=0 $u''(t)+\omega (t)f(t,u(t))=0$, u(0)=u(1)=∫01g(t)u(t)dt $u(0)=u(1)=\int _{0} ^{1}g(t)u(t)\,dt$; it turns out that this case is more difficult to handle than two point boundary value problems and needs some new ingredients...
In the current study, by using some fixed point technique such as Banach contraction principle and fixed point theorem of Krasnoselskii, we look into the positive solutions for fractional differential equation Dαcu(t) ${}^{c}D^{\alpha}u(t)$ equals to f1(t,u(t),cDβ1u(t),Iγ1u(t)) $f_{1} ( t, u(t), {}^{c}D^{ \beta_{1}} u(t), I^{\gamma_{1}} u(t) )$ and f2(t,u(t),cDβ2u(t),Iγ2u(t)) $f_{2} ( t, u(t),...
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