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

Abstract

The paper deals with the study of the existence of weak positive solutions for a new class of the system of parabolic differential equations with respect to the symmetry conditions by using sub‐super solutions method. Our results are natural extensions from our previous ones in (Bol. Soc. Mat. Mex. 2019; 25:145‐162) and (Appl. Math E‐Notes. 2018; 18:209‐218), where we have already studied the existence of positive solutions for some classes of Laplacian elliptic problems by using one classical method.

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 .…”