Existence of positive solutions for a class of $$\left( p\left( x\right) , q\left( x\right) \right) $$-Laplacian systems

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.…”

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

“…The study of differential equations and variational problems with nonstandard p ( x )−growth conditions is a new and interesting topic. It arises from nonlinear elasticity theory, electrorheological fluids, etc (see Correa and Figueiredo). Many existing results have been obtained on this kind of problems, see for example Alves and Correa and Mezouar and Boulaaras .…”

A New Proof of Existence of Positive Weak Solutions for Sublinear Kirchhoff Elliptic Systems with Multiple Parameters

“…In this work, we study the existence of weak positive solutions for a sublinear Kirchhoff elliptic systems in bounded domains by using the subsuper solutions method (SSM) combined with comparison principle which have been widely applied in many work (see for example [4,19,[21][22][23][24][25]). Validity of the comparison principle and of the SSM for local and nonlocal problems as the stationary Kirchhoff Equation was an important subject in the last few years (see, for example, [26] and [23].…”

“…en, by (24) and (25), (u, v) is a subsolution of (1). Next, we shall construct a supersolution of problem (1).…”