scholarly journals Multiplicity of Positive Solutions for Weighted Quasilinear Elliptic Equations Involving Critical Hardy-Sobolev Exponents and Concave-Convex Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Tsing-San Hsu ◽  
Huei-Li Lin
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Analysis Techniques ◽  
Multiplicity Of Positive Solutions ◽  
Quasilinear Elliptic

By variational methods and some analysis techniques, the multiplicity of positive solutions is obtained for a class of weighted quasilinear elliptic equations with critical Hardy-Sobolev exponents and concave-convex nonlinearities.

scholarly journals Existence and multiplicity results for quasilinear elliptic equations

2005 ◽  
Vol 71 (3) ◽  
pp. 377-386 ◽  
Author(s):  
Wei Dong
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Laplacian Operator ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Bounded Open Subset ◽  
Multiplicity Of Positive Solutions ◽  
Quasilinear Elliptic ◽  
Laplacian Operators

The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear elliptic equations. Based on the mountain pass theorems and sub-and supersolutions argument for p-Laplacian operators, under suitable conditions on nonlinearity f(x, s), we show the follwing problem: , where Ω is a bounded open subset of RN, N ≥ 2, with smooth boundary, λ is a positive parameter and ∆p is the p-Laplacian operator with p > 1, possesses at least two positive solutions for large λ.

scholarly journals Quasilinear Elliptic Equations with Hardy-Sobolev Critical Exponents: Existence and Multiplicity of Nontrivial Solutions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Guanwei Chen
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Critical Exponents ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Quasilinear Elliptic

We study the existence of positive solutions and multiplicity of nontrivial solutions for a class of quasilinear elliptic equations by using variational methods. Our obtained results extend some existing ones.

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*).

scholarly journals Positive Solutions for Elliptic Problems with the Nonlinearity Containing Singularity and Hardy-Sobolev Exponents

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yong-Yi Lan ◽  
Xian Hu ◽  
Bi-Yun Tang
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Semilinear Elliptic Equations ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions

In this paper, we study multiplicity of positive solutions for a class of semilinear elliptic equations with the nonlinearity containing singularity and Hardy-Sobolev exponents. Using variational methods, we establish the existence and multiplicity of positive solutions for the problem.

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