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.

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).

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.

Stable and Finite Morse Index Solutions for Dirichlet Problems with Small Diffusion in a Degenerate Case and Problems with Infinite Boundary Values

2009 ◽  
Vol 9 (4) ◽  
Author(s):  
E.N. Dancer
Keyword(s):  
Elliptic Equations ◽  
Morse Index ◽  
Nonlinear Elliptic Equations ◽  
Degenerate Case ◽  
Boundary Values ◽  
Dirichlet Problems ◽  
Small Diffusion ◽  
Weakly Nonlinear ◽  
Nonlinear Elliptic

AbstractWe consider weakly nonlinear elliptic equations with small diffusion in the case where the nonlinearity has a non-nodal zero. We show that there is an unexpected connection with problems with infinite boundary values.

Some Elliptic Problems With Degenerate Coercivity

2006 ◽  
Vol 6 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Lucio Boccardo
Keyword(s):  
Open Subset ◽  
Elliptic Equations ◽  
Principal Part ◽  
Existence Of Solutions ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Equations ◽  
Model Case ◽  
Nonlinear Elliptic ◽  
Degenerate Coercivity ◽  
Bounded Open Subset

AbstractIn this paper we are interested in existence of solutions for some nonlinear elliptic equations with principal part having degenerate coercivity. The model case iswith Ω bounded open subset of ℝ

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