Existence of positive solutions of superlinear second-order Neumann boundary value problem

Abstract

In this paper, we consider the Neumann boundary value problem { − ( p ( t ) u ′ ( t ) ) ′ + q ( t ) u ( t ) = f ( t , u ( t ) ) , t ∈ ( 0 , 1 ) u ′ ( 0 ) = u ′ ( 1 ) = 0 , where p ∈ C 1 [ 0 , 1 ] , p ( t ) > 0 , q ∈ C [ 0 , 1 ] , q ( t ) ≥ 0 , f ∈ C ( [ 0 , 1 ] × ( − ∞ , + ∞ ) , ( − ∞ , + ∞ ) ) . By using topological degree theory, we investigate the existence of nontrivial solutions. In particular, we prove the existence of positive solutions provided that q ( t ) > 0 .