Positive Solutions of Fourth-Order Problem Subject to Nonlocal Boundary Conditions

Abstract

In this paper, we study the fourth-order problem with the second derivative in nonlinearity under nonlocal boundary value conditions involving Stieltjes integrals. Some inequality conditions on nonlinearity and the spectral radius conditions of linear operators are presented that guarantee the existence of positive solutions to the problem by the theory of fixed point index on special cone. The conditions allow that the nonlinearity has superlinear or sublinear growth. Two examples are provided to support the main results under mixed boundary conditions involving multi-point with sign-changing coefficients and integral with sign-changing kernel.