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Existence and Global Behavior of Positive Solutions for Some Fourth‐Order Boundary Value Problems

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  • Ramzi S. Alsaedi

Abstract

We establish the existence and uniqueness of a positive solution to the following fourth‐order value problem: u(4)(x) = a(x)uσ(x), x ∈ (0,1) with the boundary conditions u(0) = u(1) = u′(0) = u′(1) = 0, where σ ∈ (−1,1) and a is a nonnegative continuous function on (0, 1) that may be singular at x = 0 or x = 1. We also give the global behavior of such a solution.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:657926
DOI: 10.1155/2014/657926
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