An Existence Result of Positive Solutions for Fully Second-Order Boundary Value Problems

Abstract EN

An existence result of positive solutions is obtained for the fully second-order boundary value problem - u ′′ ( t ) = f ( t , u ( t ) , u ′ ( t ) ) , t ∈ [ 0,1 ] , u ( 0 ) = u ( 1 ) = 0 , where f : [ 0,1 ] × R + × R → R is continuous.

The nonlinearity f ( t , x , y ) may be sign-changing and superlinear growth on x and y .

Our discussion is based on the method of lower and upper solution.