Multiple solutions for a quasilinear Schrödinger–Poisson system

Multiple Solutions for a Singular Quasilinear Elliptic System

We consider the multiplicity of nontrivial solutions of the following quasilinear elliptic system -div(|x|(-ap)|∇u|(p-2)∇u) + f₁(x)|u|(p-2) u = (α/(α + β))g(x)|u| (α-2) u|v| (β) + λh₁(x)|u| (γ-2) u + l₁(x), -div(|x|(-ap) |∇v| (p-2)∇v) + f₂(x)|v| (p-2) v = (β/(α + β))g(x)|v|(β-2) v|u|(α) + μh 2(x)|v|(γ-2)v + l 2(x), u(x) > 0, v(x) > 0, x ∈ ℝ(N), where λ, μ > 0, 1 < p < N, 1 < γ < p < α + β < p* ...

Existence of at least three weak solutions for a quasilinear elliptic system

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

Existence of Multiple Solutions for a Quasilinear Biharmonic Equation

Using three critical points theorems, we prove the existence of at least three solutions for a quasilinear biharmonic equation.

On Multiple Solutions for a Singular Quasilinear Elliptic System Involving Critical Hardy-sobolev Exponents

This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland’s variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz ...

Multiple Positive Radial Solutions for Quasilinear Equations in Annular Domains