Infinitely Many Solutions for Quasilinear Elliptic Problems with Broken Symmetry

2013 ◽  
Vol 13 (3) ◽  
Author(s):  
Rossella Bartolo
Keyword(s):  
Bounded Domain ◽  
Elliptic Problem ◽  
Existence Of Solutions ◽  
Elliptic Problems ◽  
Broken Symmetry ◽  
Infinitely Many Solutions ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractThe aim of this paper is investigating the existence of solutions of the quasilinear elliptic Problemwhere Ω is an open bounded domain of R

Quasilinear elliptic problems with critical exponents and Hardy terms in ℝN

2010 ◽  
Vol 53 (1) ◽  
pp. 175-193 ◽  
Author(s):  
Dongsheng Kang
Keyword(s):  
Variational Methods ◽  
Elliptic Problem ◽  
Critical Exponents ◽  
Ground State ◽  
Elliptic Problems ◽  
Ground State Solutions ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractWe deal with a singular quasilinear elliptic problem, which involves critical Hardy-Sobolev exponents and multiple Hardy terms. Using variational methods and analytic techniques, the existence of ground state solutions to the problem is obtained.

scholarly journals Regularity of Entropy Solutions of Quasilinear Elliptic Problems Related to Hardy-Sobolev Inequalities

2006 ◽  
Vol 6 (4) ◽  
Author(s):  
Boumediene Abdellaoui ◽  
Eduardo Colorado ◽  
Manel Sanchón
Keyword(s):  
Bounded Domain ◽  
Entropy Solution ◽  
Elliptic Problems ◽  
Entropy Solutions ◽  
Sobolev Inequalities ◽  
Smooth Bounded Domain ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractThis article is concerned with the regularity of the entropy solution ofwhere Ω is a smooth bounded domain Ω of ℝ

scholarly journals Infinitely many solutions for non-local problems with broken symmetry

2018 ◽  
Vol 7 (3) ◽  
pp. 353-364
Author(s):  
Rossella Bartolo ◽  
Pablo L. De Nápoli ◽  
Addolorata Salvatore
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Problem ◽  
Existence Of Solutions ◽  
Broken Symmetry ◽  
Laplacian Operator ◽  
Infinitely Many Solutions ◽  
Lipschitz Boundary ◽  
Local Problems ◽  
Non Local ◽  
Fractional Laplace Operator

AbstractThe aim of this paper is to investigate the existence of solutions of the non-local elliptic problem\left\{\begin{aligned} &\displaystyle(-\Delta)^{s}u\ =\lvert u\rvert^{p-2}u+h(% x)&&\displaystyle\text{in }\Omega,\\ &\displaystyle{u=0}&&\displaystyle\text{on }\mathbb{R}^{n}\setminus\Omega,\end% {aligned}\right.where {s\in(0,1)}, {n>2s}, Ω is an open bounded domain of {\mathbb{R}^{n}} with Lipschitz boundary {\partial\Omega}, {(-\Delta)^{s}} is the non-local Laplacian operator, {2<p<2_{s}^{\ast}} and {h\in L^{2}(\Omega)}. This problem requires the study of the eigenvalue problem related to the fractional Laplace operator, with or without potential.

Existence of Multiple Positive Solutions for N-Laplacian in a Bounded Domain in ℝN

2005 ◽  
Vol 5 (1) ◽  
Author(s):  
S. Prashanth ◽  
K. Sreenadh
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Exponential Type ◽  
Elliptic Problem ◽  
Multiplicity Result ◽  
Multiple Positive Solutions ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic

AbstractLet Ω be a bounded domain in ℝIn this article we show the existence of at least two positive solutions for the following quasilinear elliptic problem with an exponential type nonlinearity:We use Monotonicity and Variational methods to obtain this multiplicity result.

Quasilinear elliptic problems with concave–convex nonlinearities

2017 ◽  
Vol 19 (06) ◽  
pp. 1650050 ◽  
Author(s):  
M. L. M. Carvalho ◽  
Edcarlos D. da Silva ◽  
C. Goulart
Keyword(s):  
Elliptic Problem ◽  
Ground State ◽  
Nonlinear Term ◽  
Laplacian Operator ◽  
Main Difficulty ◽  
Quasilinear Elliptic Problem ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic Problems ◽  
Nehari Method ◽  
Quasilinear Elliptic

In this paper, the existence and multiplicity of solutions for a quasilinear elliptic problem driven by the [Formula: see text]-Laplacian operator is established. These solutions are also built as ground state solutions using the Nehari method. The main difficulty arises from the fact that the [Formula: see text]-Laplacian operator is not homogeneous and the nonlinear term is indefinite.

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