Existence of Positive Solutions and Its Asymptotic Behavior of (p(x), q(x))-Laplacian Parabolic System

Abstract

This paper deals with the existence of positively solution and its asymptotic behavior for parabolic system of ( p ( x ) , q ( x ) ) -Laplacian system of partial differential equations using a sub and super solution according to some given boundary conditions, Our result is an extension of Boulaaras’s works which studied the stationary case, this idea is new for evolutionary case of this kind of problem.

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

“…In this work, the existence and nonexistence of positive weak solution are proved for the elliptic systems involving (p 1 , … , p m ) Laplacian operator with zero Dirichlet boundary condition in bounded domain Ω ⊂ R N by using subsuper solutions method, which has been widely applied in many work (see, for example, previous studies). 7,[16][17][18][19][20] The obtained results are natural generalization and extension of previous work. 5,8,[13][14][15] In our next study, we will try to apply an alternative approach using the variational principle that has been presented in previous studies.…”

“…In this work, the existence and nonexistence of positive weak solution are proved for the elliptic systems involving Laplacian operator with zero Dirichlet boundary condition in bounded domain by using subsuper solutions method, which has been widely applied in many work (see, for example, previous studies) . The obtained results are natural generalization and extension of previous work .…”

Existence of positive solutions of (p(x),q(x))‐Laplacian parabolic systems with right hand side defined as a multiplication of two separate functions

“…Moreover, in Azouz and Bensedik and Mezouar and Boulaaras, the authors studied the existence of solutions for problem , where some symmetry conditions are imposed. Then, Medekhel et al investigated the existence of positive solutions of the system without any symmetry conditions. Motivated by the ideas introduced in Medekhel et al where the authors proved the existence of a positive solution when λ is large enough and satisfies the condition and they did not assume any symmetric condition, and did not assume any sign condition on f (0) and g (0).…”

“…without any symmetry conditions. Motivated by the ideas introduced in Medekhel et al 18 where the authors proved the existence of a positive solution when is large enough and satisfies the condition (4) and they did not assume any symmetric condition, and did not assume any sign condition on f(0) and g(0). Also, the authors proved the existence of positive solutions with multiparameter.…”

Existence of Positive Solutions for a Class ofpx,qx-Laplacian Elliptic Systems with

“…Knobloch in [20] introduced the sub-supersolution method to the study of periodic boundary value problems for nonlinear second-order ordinary differential equations using Cesari's method; similar problems and techniques were studied in [21,22] and still the sub-supersolutions and supersolutions are assumed to be smooth solutions of differential inequalities. en, the SSM were also used to study Dirichlet and Neumann boundary value problems for semilinear elliptic problems in [23,24], and even for nonlinear boundary value problems in [25][26][27] and also for systems of nonlinear ordinary differential equations in [28][29][30].…”