Existence results for a class of degenerate quasilinear elliptic systems

Existence of positive weak solution for a weighted system of autocatalytic reaction steady state type

“…So, equation ( 9) is satisfy and ψ is a weak subsolution of (1). Next, we construct a weak supersolution z of system (1). Let e p = e p (x) be the positive weak solution of (see [25]) (13) −∆ P,p e p = 1 in Ω, e p = 0 on ∂Ω.…”

“…In this paper, we are concerned with the existence and nonexistence results of positive weak solution for the weighted p-Laplacian autocatalytic reaction problem (1) −∆ P,p u = λm(x)[νa(x)u α − υu β ] in Ω u = 0 on ∂Ω.…”

“…Systems of type (1), with certian values for P (x), p, α, β, have received considerable attention in the last decade (see, e.g., [12,21,22,24] and the references therein). It has been shown that for some certian values of α, β, the system (1) has a rich mathematical structure.…”

“…On the other hand, the existence of weak solutions for nonlinear elliptice systems involving p-Laplacian operators with different weights has been studied using an approximation method (see [25]), the theory of nonlinear monotone operators method (see [26]) and the sub-supersolutions method (see [10,11,14,19,20]). Recently, the behaviours and properties of the weak solution for some nonlinear systems have received considerable attention (see [1,[15][16][17][18])…”

Existence and stability of positive weak solutions for a class of chemically reacting systems

“…Systems of singular equations such as (1) represent the stationary counterpart of general evolutionary problems of the form:…”