scholarly journals Multiplicity results for some nonlinear elliptic problems

2004 ◽  
Vol 76 (2) ◽  
pp. 247-268
Author(s):  
Kuan-Ju Chen
Keyword(s):  
Ground State ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Ground State Solution ◽  
State Solution ◽  
Energy Solution ◽  
Nonlinear Elliptic Problems ◽  
Multiplicity Results ◽  
Nonlinear Elliptic ◽  
Half Strip

AbstractIn this paper, first, we study the existence of the positive solutions of the nonlinear elliptic equations in unbounded domains. The existence is affected by the properties of the geometry and the topology of the domain. We assert that if there exists a (PS)c-sequence with c belonging to a suitable interval depending by the equation, then a ground state solution and a positive higher energy solution exist, too. Next, we study the upper half strip with a hole. In this case, the ground state solution does not exist, however there exists at least a positive higher energy solution.

scholarly journals Multiplicity Results for Some Nonlinear Elliptic Equations

1996 ◽  
Vol 137 (1) ◽  
pp. 219-242 ◽  
Author(s):  
Antonio Ambrosetti ◽  
Jesus Garcia Azorero ◽  
Ireneo Peral
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Multiplicity Results ◽  
Nonlinear Elliptic

Multiple Positive Solutions For a Class of Nonlinear Elliptic Equations

2006 ◽  
Vol 6 (1) ◽  
Author(s):  
Shenghua Weng ◽  
Yongqing Li
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Nonlinear Elliptic Equations ◽  
Multiple Positive Solutions ◽  
Combined Effects ◽  
Multiplicity Results ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

AbstractThis paper deals with a class of nonlinear elliptic Dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results.

Multiplicity results for nonlinear elliptic equations involving critical Sobolev exponent

1986 ◽  
Vol 103 (3-4) ◽  
pp. 275-285 ◽  
Author(s):  
A. Capozzi ◽  
G. Palmieri
Keyword(s):  
Elliptic Equations ◽  
Multiple Solutions ◽  
Nonlinear Elliptic Equations ◽  
Critical Sobolev Exponent ◽  
Sobolev Embedding ◽  
Multiplicity Results ◽  
Variational Techniques ◽  
Nonlinear Elliptic ◽  
Sobolev Exponent ◽  
Image Position

SynopsisIn this paper we study the following boundary value problemwhere Ω is a bounded domain in Rn, n≧3, x ∈Rn, p* = 2n/(n – 2) is the critical exponent for the Sobolev embedding is a real parameter and f(x, t) increases, at infinity, more slowly than .By using variational techniques, we prove the existence of multiple solutions to the equations (0.1), in the case when λ belongs to a suitable left neighbourhood of an arbitrary eigenvalue of −Δ, and the existence of at least one solution for any λ sufficiently large.

scholarly journals On a nonlinear elliptic problems having large monotonocity with L1-data in weighted Orlicz-Sobolev spaces

2019 ◽  
Vol 5 (1) ◽  
pp. 104-116
Author(s):  
Badr El Haji ◽  
Mostafa El Moumni ◽  
Khaled Kouhaila
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Entropy Solution ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Equations ◽  
Monotonicity Condition ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Right Hand ◽  
L1 Data

AbstractWe prove in weighted Orlicz-Sobolev spaces, the existence of entropy solution for a class of nonlinear elliptic equations of Leray-Lions type, with large monotonicity condition and right hand side f ∈ L1(Ω).

Remarks on Nonlinear Elliptic Problems on Long Domains

2005 ◽  
Vol 5 (2) ◽  
Author(s):  
E.N. Dancer
Keyword(s):  
Elliptic Equations ◽  
Turning Point ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Equations ◽  
Homoclinic Solutions ◽  
Local Uniqueness ◽  
Nonlinear Elliptic Problems ◽  
Weakly Nonlinear ◽  
Nonlinear Elliptic ◽  
Domain Length

AbstractIn this paper, we discuss the behaviour of solutions near a turning point for weakly nonlinear elliptic equations on long domains. We are looking for results independent of the domain length. In the process we obtain some local uniqueness and non-degeneracy results for homoclinic solutions on infinite strips.

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