Existence of Positive Solutions for Some Superlinear Fourth-Order Boundary Value Problems

Abstract

We are concerned with the following superlinear fourth-order equationu4t+utφt,−ut=0,   t∈0, 1;−u0=u1=0,  −u′0=a,  −u′1=-b, wherea,−bare nonnegative constants such thata+b>0andφt,−sis a nonnegative continuous function that is required to satisfy some appropriate conditions related to a classKsatisfying 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.