scholarly journals The Nehari manifold and the existence of multiple solutions for a singular quasilinear elliptic equation

2012 ◽  
Vol 393 (2) ◽  
pp. 671-679 ◽  
Author(s):  
Caisheng Chen ◽  
Zonghu Xiu ◽  
Jincheng Huang
Keyword(s):  
Elliptic Equation ◽  
Multiple Solutions ◽  
Quasilinear Elliptic Equation ◽  
Nehari Manifold ◽  
The Nehari Manifold ◽  
Quasilinear Elliptic

scholarly journals Multiple Solutions for the p(x)− Laplace Operator with Critical Growth

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Analia Silva
Keyword(s):  
Elliptic Equation ◽  
Laplace Operator ◽  
Multiple Solutions ◽  
Variable Exponent ◽  
Quasilinear Elliptic Equation ◽  
Critical Growth ◽  
Nontrivial Solutions ◽  
Multiplicity Of Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractThe aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation −Δ

scholarly journals Multiple Solutions of Quasilinear Elliptic Equations in

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Huei-li Lin
Keyword(s):  
Elliptic Equation ◽  
Ground State ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Quasilinear Elliptic Equation ◽  
Ground State Solution ◽  
The Other ◽  
Quasilinear Elliptic Equations ◽  
Positive Continuous Function ◽  
Quasilinear Elliptic

Assume that is a positive continuous function in and satisfies some suitable conditions. We prove that the quasilinear elliptic equation in admits at least two solutions in (one is a positive ground-state solution and the other is a sign-changing solution).

scholarly journals Multiple solutions for a coercive quasilinear elliptic equation via Morse theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lifang Fu ◽  
Mingzheng Sun
Keyword(s):  
Elliptic Equation ◽  
Elliptic Problem ◽  
Morse Theory ◽  
Multiple Solutions ◽  
Quasilinear Elliptic Equation ◽  
Nontrivial Solutions ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic

AbstractWe study the quasilinear elliptic problem which is resonant at zero. By using Morse theory, we obtain five nontrivial solutions for the equation with coercive nonlinearities.

scholarly journals Multiplicity of positive solutions for quasilinear elliptic equations involving critical nonlinearity

2020 ◽  
Vol 9 (1) ◽  
pp. 1420-1436
Author(s):  
Xiangdong Fang ◽  
Jianjun Zhang
Keyword(s):  
Positive Solutions ◽  
Category Theory ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Nehari Manifold ◽  
Quasilinear Elliptic Equations ◽  
Critical Nonlinearity ◽  
Multiplicity Of Positive Solutions ◽  
The Nehari Manifold ◽  
Quasilinear Elliptic

Abstract We are concerned with the following quasilinear elliptic equation $$\begin{array}{} \displaystyle -{\it\Delta} u-{\it\Delta}(u^{2})u=\mu |u|^{q-2}u+|u|^{2\cdot 2^*-2}u, u\in H_0^1({\it\Omega}), \end{array}$$(QSE) where Ω ⊂ ℝN is a bounded domain, N ≥ 3, qN < q < 2 ⋅ 2∗, 2∗ = 2N/(N – 2), qN = 4 for N ≥ 6 and qN = $\begin{array}{} \frac{2(N+2)}{N-2} \end{array}$ for N = 3, 4, 5, and μ is a positive constant. By employing the Nehari manifold and the Lusternik-Schnirelman category theory, we prove that there exists μ* > 0 such that (QSE) admits at least catΩ(Ω) positive solutions when μ ∈ (0, μ*).

Sign in / Sign up

Export Citation Format

Share Document