SINGULAR LIMITS FOR 2-DIMENSIONAL ELLIPTIC PROBLEM WITH EXPONENTIALLY DOMINATED NONLINEARITY AND SINGULAR DATA

2011 ◽  
Vol 13 (04) ◽  
pp. 697-725 ◽  
Author(s):  
SAMI BARAKET ◽  
INES BEN OMRANE ◽  
TAIEB OUNI ◽  
NIHED TRABELSI
Keyword(s):  
Boundary Condition ◽  
Elliptic Problem ◽  
Source Term ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Singular Limits ◽  
Singular Source ◽  
Singular Data

We study existence of solutions with singular limits for a 2-dimensional semilinear elliptic problem with exponential dominated nonlinearity and a singular source term given by Dirac masses, imposing Dirichlet boundary condition. This paper extends previous results obtained in [3, 8]. We mainly use the method of domain decomposition.

scholarly journals Singular Limits for 2-Dimensional Elliptic Problem with Exponentially Dominated Nonlinearity and a Quadratic Convection Term

2013 ◽  
Vol 21 (1) ◽  
pp. 19-50
Author(s):  
Sami Baraket ◽  
Imen Bazarbacha ◽  
Saber Kharrati ◽  
Taieb Ouni
Keyword(s):  
Elliptic Problem ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Gradient Term ◽  
Two Dimensional ◽  
Convection Term ◽  
Linear Gradient ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Singular Limits

Abstract We study existence of solutions with singular limits for a two-dimensional semilinear elliptic problem with exponential dominated nonlinearity and a quadratic convection non linear gradient term, imposing Dirichlet boundary condition. This paper extends previous results obtained in [1], [3], [4] and some references therein for related issues.

scholarly journals Multiplicity of solutions for singular semilinear elliptic equations with critical Hardy-Sobolev exponents

2008 ◽  
Vol 2 (2) ◽  
pp. 158-174 ◽  
Author(s):  
Qianqiao Guo ◽  
Pengcheng Niu ◽  
Jingbo Dou
Keyword(s):  
Boundary Condition ◽  
Variational Methods ◽  
Elliptic Problem ◽  
Dirichlet Boundary Condition ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

We consider the semilinear elliptic problem with critical Hardy-Sobolev exponents and Dirichlet boundary condition. By using variational methods we obtain the existence and multiplicity of nontrivial solutions and improve the former results.

Semilinear Robin problems resonant at both zero and infinity

2018 ◽  
Vol 30 (1) ◽  
pp. 237-251
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Boundary Condition ◽  
Variational Methods ◽  
Elliptic Problem ◽  
Robin Boundary Condition ◽  
Critical Groups ◽  
Smooth Solutions ◽  
Reaction Term ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Robin Boundary

Abstract We consider a semilinear elliptic problem, driven by the Laplacian with Robin boundary condition. We consider a reaction term which is resonant at {\pm\infty} and at 0. Using variational methods and critical groups, we show that under resonance conditions at {\pm\infty} and at zero the problem has at least two nontrivial smooth solutions.

scholarly journals Existence of Solutions to a Class of Semilinear Elliptic Problem with Nonlinear Singular Terms and Variable Exponent

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Ying Chu ◽  
Yanchao Gao ◽  
Wenjie Gao
Keyword(s):  
Variable Exponent ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Dirichlet Boundary Value Problem ◽  
Lebesgue Spaces ◽  
Singular Terms ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Existence And Regularity Results ◽  
Regularity Results

The authors of this paper prove the existence and regularity results for the homogeneous Dirichlet boundary value problem to the equation- div(M(x)∇un)=f(x)/uα(x)withf∈Lm(Ω)  (m⩾…1)andα(x)>0. The results show the dependence of the summability offin some Lebesgue spaces and on the values ofα(x).

scholarly journals Existence of solutions for some degenerate semilinear elliptic equations with measure data

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 23-31
Author(s):  
Badajena Arun Kumar ◽  
Pradhan Shesadev
Keyword(s):  
Weak Solution ◽  
Elliptic Problem ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Semilinear Elliptic Equations ◽  
Measure Data ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

We study the existence of a weak solution for a certain degenerate semilinear elliptic problem.

A Priori Bounds and Existence of Solutions for Slightly Superlinear Elliptic Problems

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
J. García-Melián ◽  
L. Iturriaga ◽  
H. Ramos Quoirin
Keyword(s):  
Continuous Function ◽  
Positive Solution ◽  
Critical Points ◽  
Elliptic Problem ◽  
Existence Of Solutions ◽  
A Priori ◽  
A Priori Bounds ◽  
Abstract Theorem ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

AbstractWe consider the semilinear elliptic problemwhere a is a continuous function which may change sign and f is superlinear but does not satisfy the standard Ambrosetti-Rabinowitz condition. We show that if f is regularly varying of index one at infinity then the above problem has a positive solution, provided α satisfies some additional assumptions. Our proof uses an abstract theorem due to L. Jeanjean on critical points of functionals with mountain-pass structure, and it relies on the obtention of a priori bounds for positive solutions..

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