Symmetric positive solutions of boundary value problems with integral boundary conditions

Under conditions weaker than those used by Ma, we establish various results on the existence and nonexistence of symmetric positive solutions to fourth-order boundary value problems with integral boundary conditions. The arguments are based upon a specially constructed cone and the fixed point theory in a cone. Our results improve and extend that obtained in [H. Ma, Symmetric positive solutions for nonlocal boundary value problems of fourth order, Nonlinear Anal. 68 (2008) 645–651]. We illustrate our results by one example, which cannot be handled using the existing results.