Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments

Zhaocai Hao and Yubo Huang

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments Dαx(t) + μh(t)f(x(a(t))) = 0, t ∈ (0,1), 2 0, x(0) = x′(0) = 0, x(1) = βx(η) + λ[x], β > 0, η ∈ (0,1), where Dα is the standard Riemann‐Liouville derivative, f : [0, ∞)→[0, ∞) is continuous, f(0) > 0, h : [0,1]→(−∞, +∞), and a(t) is the advanced argument. Our analysis relies on a nonlinear alternative of Leray‐Schauder type. An example is given to illustrate our results.

Date: 2014
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https://doi.org/10.1155/2014/158436

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:158436

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