Existence and non-existence of positive solution for (p, q)-Laplacian with singular weights

Abstract

abstract:We use the Hardy-Sobolev inequality to study existence and nonexistence results for a positive solution of the quasilinear elliptic problemdriven by nonhomogeneous operator (p, q)-Laplacian with singular weights under the Dirichlet boundary condition. We also prove that in the case where µ > 0 and with 1 < q < p < ∞ the results are completely different from those for the usual eigenvalue problem for the p-Laplacian with singular weight under the Dirichlet boundary condition, which is retrieved when µ = 0. Precisely, we show that when µ > 0 there exists an interval of eigenvalues for our eigenvalue problem.

On a positive solution for $(p,q)$-Laplace equation with Nonlinear

“…A non-existence result is also given. In [18], A. Zerouali and B. Karim are proved the same results by assuming the singularities on the domain and the weights. Our purpose in this article is to extend the results of the classical eigenvalue problem involving the (p, q)-Laplacian (see for example [11,12]) and generalize some results knouwn in the classical p-Laplacian Steklov problems (see [4]).…”

On sign-changing solutions for (p,q)-Laplace equations with two parameters

“…The considered problem (GEV ; α, β) attracts special attention due to its symmetric and partially homogeneous structure, cf. [31,32,27,20,34,10,4]. By developing the results of [31,27,20], the authors of the present article obtained in [10] a reasonably complete description of the subsets of the (α, β)-plane which correspond to the existence/nonexistence of positive solutions to the problem (GEV ; α, β).…”