An asymptotic behavior of positive solutions for a new class of elliptic systems involving of $$\left( p\left( x\right) ,q\left( x\right) \right) $$ p x , q x -Laplacian systems

Some existence results for an elliptic equation of Kirchhoff‐type with changing sign data and a logarithmic nonlinearity

“…Our results are natural extensions from the previous recent ones, [7][8][9]11 where the authors have already studied the existence of positive solutions for some classes of Laplacian elliptic problems by using one classical method which is sub-supersolution. Here, in addition to the latter method, we use two other known methods, a direct variational method and Galerkin approach for proving some existence results to a logarithmic nonlinear elliptic equation of Kirchhoff-type with changing sign data.…”

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.…”

Existence of Positive Solutions of Nonlocal p(x)-Kirchhoff Evolutionary Systems via Sub-Super Solutions Concept

“…where ρ, P 0 , h, E, L are constants, which extends the classical D'Alembert's wave equation, by considering the effects of the changes in the length of the strings during the vibrations. In recent years, problems involving Kirchhoff type operators have been studied in many papers, we refer to [14][15][16][17][18][19][20][21], in which the authors have used a variational method and topological method to get the existence of solutions. In this paper, motivated by the ideas introduced in [22] and the properties of Kirchhoff type operators in [22], we study the existence of positive solutions for system (2) by using the sub-and super solutions techniques.…”