On Existence of L∞-Ground States for Singular Elliptic Equations in the Presence of a Strongly Nonlinear Term

2007 ◽  
Vol 7 (3) ◽  
Author(s):  
J.V. Goncalves ◽  
A.L. Melo ◽  
C.A. Santos
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Nonlinear Term ◽  
Ground States ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Singular Elliptic Equations

AbstractWe establish new results concerning existence and the behavior at infinity of solutions for the singular nonlinear elliptic equation −Δu = ρa(x)u

scholarly journals Existence of solutions for elliptic equations having natural growth terms in Orlicz spaces

2004 ◽  
Vol 2004 (12) ◽  
pp. 1031-1045 ◽  
Author(s):  
A. Elmahi ◽  
D. Meskine
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Natural Growth ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Natural Growth Terms

Existence result for strongly nonlinear elliptic equation with a natural growth condition on the nonlinearity is proved.

Nonlinear Elliptic Equations in Strip-Like Domains

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Jaeyoung Byeon ◽  
Kazunaga Tanaka
Keyword(s):  
Elliptic Equation ◽  
Positive Solution ◽  
Bounded Domain ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic

AbstractWe study the existence of a positive solution of a nonlinear elliptic equationwhere k ≥ 2 and D is a bounded domain domain in R

Nonlinear elliptic equations with critical potential and critical parameter

2006 ◽  
Vol 136 (5) ◽  
pp. 1041-1051 ◽  
Author(s):  
Yao Tian Shen ◽  
Yang Xin Yao
Keyword(s):  
Elliptic Equation ◽  
Hardy Space ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Critical Parameter ◽  
Nonlinear Elliptic Equations ◽  
Point Theory ◽  
Positive Answer ◽  
Critical Potential ◽  
Nonlinear Elliptic

We give a positive answer to an open problem about Hardy's inequality raised by Brézis and Vázquez, and another result obtained improves that of Vázquez and Zuazua. Furthermore, by this improved inequality and the critical-point theory, in a k-order Sobolev–Hardy space, we obtain the existence of multi-solution to a nonlinear elliptic equation with critical potential and critical parameter.

scholarly journals MULTIPLE CONDENSATIONS FOR A NONLINEAR ELLIPTIC EQUATION WITH SUB-CRITICAL GROWTH AND CRITICAL BEHAVIOUR

2001 ◽  
Vol 44 (3) ◽  
pp. 631-660 ◽  
Author(s):  
Juncheng Wei
Keyword(s):  
Elliptic Equation ◽  
Critical Points ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Nonlinear Elliptic Equations ◽  
Subject Classification ◽  
Critical Behaviour ◽  
Unknown Constant ◽  
Secondary 35J40 ◽  
Nonlinear Elliptic

AbstractWe consider the following nonlinear elliptic equations\begin{gather*} \begin{cases} \Delta u+u_{+}^{N/(N-2)}=0\amp\quad\text{in }\sOm, \\ u=\mu\amp\quad\text{on }\partial\sOm\quad(\mu\text{ is an unknown constant}), \\ \dsty\int_{\partial\sOm}\biggl(-\dsty\frac{\partial u}{\partial n}\biggr)=M, \end{cases} \end{gather*}where $u_{+}=\max(u,0)$, $M$ is a prescribed constant, and $\sOm$ is a bounded and smooth domain in $R^N$, $N\geq3$. It is known that for $M=M_{*}^{(N)}$, $\sOm=B_R(0)$, the above problem has a continuum of solutions. The case when $M>M_{*}^{(N)}$ is referred to as supercritical in the literature. We show that for $M$ near $KM_{*}^{(N)}$, $K>1$, there exist solutions with multiple condensations in $\sOm$. These concentration points are non-degenerate critical points of a function related to the Green's function.AMS 2000 Mathematics subject classification: Primary 35B40; 35B45. Secondary 35J40

scholarly journals FOUNTAIN-LIKE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS WITH CRITICAL GROWTH AND HARDY POTENTIAL

2005 ◽  
Vol 07 (06) ◽  
pp. 867-904 ◽  
Author(s):  
VERONICA FELLI ◽  
SUSANNA TERRACINI
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Blow Up ◽  
Nonlinear Elliptic Equations ◽  
Critical Growth ◽  
Hardy Potential ◽  
Nonlinear Elliptic ◽  
Hardy Type ◽  
Type Potential

We prove the existence of fountain-like solutions, obtained by superposition of bubbles of different blow-up orders, for a nonlinear elliptic equation with critical growth and Hardy-type potential.

scholarly journals Existence of entropy solutions for some nonlinear elliptic problems involving variable exponent and measure data

2018 ◽  
Vol 36 (2) ◽  
pp. 33-55 ◽  
Author(s):  
Taghi Ahmedatt ◽  
Elhoussine Azroul ◽  
Hassane Hjiaj ◽  
Abdelfattah Touzani
Keyword(s):  
Elliptic Equation ◽  
Variable Exponent ◽  
Nonlinear Term ◽  
Entropy Solutions ◽  
Measure Data ◽  
Nonlinear Elliptic Problems ◽  
Strongly Nonlinear ◽  
Nonstandard Growth ◽  
Nonlinear Elliptic ◽  
Nonstandard Growth Condition

In this paper, we study the existence of entropy solutions for some nonlinear $p(x)-$elliptic equation of the type $$Au - \mbox{div }\phi(u) + H(x,u,\nabla u) = \mu,$$ where $A$ is an operator of Leray-Lions type acting from $W_{0}^{1,p(x)}(\Omega)$ into its dual, the strongly nonlinear term $H$ is assumed only to satisfy some nonstandard growth condition with respect to $|\nabla u|,$ here $\>\phi(\cdot)\in C^{0}(I\!\!R,I\!\!R^{N})\>$ and $\mu$ belongs to ${\mathcal{M}}_{0}^{b}(\Omega)$.

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