Non-trivial solutions for nonlocal elliptic problems of Kirchhoff-type

2016 ◽  
Vol 23 (3) ◽  
pp. 293-301
Author(s):  
Ghasem A. Afrouzi ◽  
Armin Hadjian
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Elliptic Problems ◽  
Existence Results ◽  
Kirchhoff Type ◽  
Nonlocal Elliptic Problem

AbstractExistence results of positive solutions for a nonlocal elliptic problem of Kirchhoff-type are established. The approach is based on variational methods.

Asymptotic behaviour of positive solutions of semilinear elliptic problems with increasing powers

2021 ◽  
pp. 1-18
Author(s):  
Lucio Boccardo ◽  
Liliane Maia ◽  
Benedetta Pellacci
Keyword(s):  
Linear Operator ◽  
Asymptotic Behaviour ◽  
Positive Solutions ◽  
Elliptic Problems ◽  
Existence Results ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Image Position

We prove existence results of two solutions of the problem \[ \begin{cases} L(u)+u^{m-1}=\lambda u^{p-1} & \text{in}\ \Omega,\\ u>0 & \text{in}\ \Omega,\\ u=0 & \text{on}\ \partial \Omega, \end{cases} \] where $L(v)=-\textrm {div}(M(x)\nabla v)$ is a linear operator, $p\in (2,2^{*}]$ and $\lambda$ and $m$ sufficiently large. Then their asymptotical limit as $m\to +\infty$ is investigated showing different behaviours.

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.

scholarly journals Existence and Concentration of Solutions for a Class of Elliptic Problems with Discontinuous Nonlinearity in $\mathbf{R}^{N}$

2013 ◽  
Vol 112 (1) ◽  
pp. 129 ◽  
Author(s):  
Claudianor O. Alves ◽  
Rúbia G. Nascimento
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Problems ◽  
Discontinuous Nonlinearity ◽  
Concentration Of Solutions

Using variational methods we establish existence and concentration of positive solutions for a class of elliptic problems in $\mathbf{R}^{N}$, whose nonlinearity is discontinuous.

scholarly journals Existence results for a class of Kirchhoff type systems with Caffarelli-Kohn-Nirenberg exponents

2016 ◽  
Vol 24 (1) ◽  
pp. 83-94
Author(s):  
G. A. Afrouzi ◽  
H. Zahmatkesh ◽  
S. Shakeri
Keyword(s):  
Positive Solution ◽  
Positive Solutions ◽  
Type Systems ◽  
Existence Results ◽  
Kirchhoff Type ◽  
Existence Of Positive Solutions ◽  
Singular Weights

Abstract This paper is concerned with the existence of positive solutions for a class of infinite semipositone kirchhoff type systems with singular weights. Our aim is to establish the existence of positive solution for λ large enough. The arguments rely on the method of sub-and super-solutions.

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.

scholarly journals A VARIATIONAL APPROACH FOR A BI-NON-LOCAL ELLIPTIC PROBLEM INVOLVING THE p(x)-LAPLACIAN AND NON-LINEARITY WITH NON-STANDARD GROWTH

2013 ◽  
Vol 56 (2) ◽  
pp. 317-333 ◽  
Author(s):  
FRANCISCO JULIO S. A. CORRÊA ◽  
AUGUSTO CÉSAR DOS REIS COSTA
Keyword(s):  
Variational Principle ◽  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Variational Approach ◽  
Mountain Pass Theorem ◽  
Ekeland Variational Principle ◽  
Existence Of Positive Solutions ◽  
Non Local ◽  
Local Term

AbstractIn this paper we are concerned with a class of p(x)-Kirchhoff equation where the non-linearity has non-standard growth and contains a bi-non-local term. We prove, by using variational methods (Mountain Pass Theorem and Ekeland Variational Principle), several results on the existence of positive solutions.

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.

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