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.
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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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