Electron. J. Differential Equations, Vol. 2017 (2017), No. 215, pp. 1-23.

Multiplicity of solutions for non-homogeneous Neumann problems in Orlicz-Sobolev spaces

Shapour Heidarkhani, Massimiliano Ferrara, Giuseppe Caristi, Johnny Henderson, Amjad Salari

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.

Submitted February 22, 2017. Published September 13, 2017.
Math Subject Classifications: 35D05, 35J60, 35J70, 46N20, 58E05, 68T40, 76A02.
Key Words: Multiplicity results; weak solution; Orlicz-Sobolev space; non-homogeneous Neumann problem; variational methods; critical point theory.

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Shapour Heidarkhani
Department of Mathematics
Faculty of sciences, Razi University
67149 Kermanshah, Iran
email: s.heidarkhani@razi.ac.ir
Massimiliano Ferrara
Department of Law and Economics
University Mediterranea of Reggio Calabria
Via dei Bianchi, 2 - 89131 Reggio Calabria, Italy
email: massimiliano.ferrara@unirc.it
Giuseppe Caristi
Department of Economics
University of Messina
via dei Verdi, 75, Messina, Italy
email: gcaristi@unime.it
Johnny Henderson
Department of Mathematics
Baylor University
Waco, TX 76798-7328, USA
email: Johnny_Henderson@baylor.edu
Amjad Salari
Department of Mathematics
Faculty of sciences, Razi University
67149 Kermanshah, Iran
email: amjads45@yahoo.com

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