MULTIPLICITY OF SOLUTIONS FOR NON-HOMOGENEOUS NEUMANN PROBLEMS IN ORLICZ-SOBOLEV SPACES

作者：Heidarkhani Shapour^*; Ferrara Massimiliano; Caristi Giuseppe; Henderson Johnny; Salari Amjad

来源：Electronic Journal of Differential Equations, 2017, 215.

• Multiplicity results
• weak solution
• Orlicz-Sobolev space
• non-homogeneous Neumann problem
• variational methods
• critical point theory

This article concerns the existence of non-trivial weak solutions for a class of non-homogeneous Neumann problems. The approach is through variational methods and critical point theory in Orlicz-Sobolev spaces. We investigate the existence of two solutions for the problem under some algebraic conditions with the classical Ambrosetti-Rabinowitz condition on the nonlinear term and using a consequence of the local minimum theorem due to Bonanno and mountain pass theorem. Furthermore, by combining two algebraic conditions on the nonlinear term and employing two consequences of the local minimum theorem due Bonanno we ensure the existence of two solutions, by applying the mountain pass theorem of Pucci and Serrin, we set up the existence of the third solution for the problem.

• 出版日期2017-9-13