Subsuper solutions method for elliptic systems involving p1,...,pm Laplacian operator

Abstract

In this paper, we prove the existence and nonexistence of positive weak solution for a generalized elliptic systems involving ()p1,…,pm Laplacian operator with zero Dirichlet boundary condition in bounded domain normalΩ⊂double-struckRN by using subsuper solutions method. Our results are natural generalization and extension of previous studies.

New existence result of positive solutions for a class of fractional Kirchhoff-type systems with multiple parameters

“…In a recent paper [20], the author has extended the results in [2,3] to elliptic system with multiple parameters and nonlinear boundary conditions. Rafik and Salah in [14] extended the study of [4,5] to the generalized elliptic systems involving (p 1 , ..., p m )−Laplacian operator with zero Dirichlet boundary condition in bounded domain.…”

“…It is well known that the sub and super solution method is a very efficient tool for dealing with the existence of solutions of nonlinear problems ( [1,3,14,15,16]). However, there are few results on BVPs for fractional Laplacian problems via sub and super solutions method and no paper is concerned with the existence results of positive solutions of fractional Kirchhoff-type systems via sub and super solutions method.…”

Existence and multiplicity of positive weak solutions for a new class of (P; Q)-Laplacian systems

“…(see [5], [15] [1]- [6]). A lot of existence results have been obtained on this class of problems, we refer to ( [4], [5], [7], [10], [13], [14], [3], [2], [11], [9], [8]). These problems originate from physical models and are widely used in many fields such as combustion, mathematical biology, chemical reactions and so on.…”

Existence and multiplicity of positive weak solutions for a new class of $(p; q)$-Laplacian systems

“…(see [1]- [4], [5] [8], [9], [22] and [24]). A lot of existence results have been obtained on this class of problems, we refer to ( [6], [7], [8], [10], [11], [12], [13], [17], [21], [20], [23]). These problems originate from physical models and are widely used in many fields such as combustion, mathematical biology, chemical reactions and so on.…”

“…These problems originate from physical models and are widely used in many fields such as combustion, mathematical biology, chemical reactions and so on. Our method is mainly focused on the method of sub-super solutions (see [17], [21] for a more detailed discussion).…”