Existence and Global Behavior of Positive Solutions for Some Fourth-Order Boundary Value Problems - Ramzi S. Alsaedi (Abstract and Applied Analysis)
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.