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
Abstract:
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.
Show me the PDF file (329 KB),
TEX file for this article.
 |
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
|
|---|
Return to the EJDE web page