Existence of Positive Solutions for Some Superlinear Fourth-Order Boundary Value Problems - Imed Bachar; Habib Mâagli (Journal of Function Spaces)
We are concerned with the following superlinear fourth-order equation u4t+utφt,−ut=0,    t∈0, 1; −u0=u1=0,  −u′0=a,  − u′1=-b, where a,−b are nonnegative constants such that a+b>0 and φt,−s is a nonnegative continuous function that is required to satisfy some appropriate conditions related to a class K satisfying suitable integrability condition. Our purpose is to prove the existence, uniqueness, and global behavior of a classical positive solution to the above problem by using a method based on estimates on the Green function and perturbation arguments.