Applications to Elliptic Problems in Bounded Domains

2001 ◽  
pp. 81-111
Author(s):  
Maria do Rosário Grossinho ◽  
Stepan Agop Tersian
Keyword(s):  
Elliptic Problems ◽  
Bounded Domains

scholarly journals Normal solvability of general linear elliptic problems

2005 ◽  
Vol 2005 (7) ◽  
pp. 733-756 ◽  
Author(s):  
A. Volpert ◽  
V. Volpert
Keyword(s):  
Elliptic Problems ◽  
Unbounded Domains ◽  
General Linear ◽  
Bounded Domains ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Ellipticity Condition ◽  
Normal Solvability ◽  
General Elliptic ◽  
Necessary And Sufficient

The paper is devoted to general elliptic problems in the Douglis-Nirenberg sense. We obtain a necessary and sufficient condition of normal solvability in the case of unbounded domains. Along with the ellipticity condition, proper ellipticity and Lopatinsky condition that determine normal solvability of elliptic problems in bounded domains, one more condition formulated in terms of limiting problems should be imposed in the case of unbounded domains.

Existence and Regularity Results for Anisotropic Elliptic Problems

2009 ◽  
Vol 9 (2) ◽  
Author(s):  
Agnese Di Castro
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Elliptic Problems ◽  
Dirichlet Boundary Conditions ◽  
Bounded Domains ◽  
Existence And Regularity Results ◽  
Regularity Results ◽  
Homogeneous Dirichlet Boundary Conditions

AbstractWe study existence and regularity of the solutions for some anisotropic elliptic problems with homogeneous Dirichlet boundary conditions in bounded domains.

scholarly journals Existence of Strictly Positive Solutions for Sublinear Elliptic Problems in Bounded Domains

2014 ◽  
Vol 14 (2) ◽  
Author(s):  
T. Godoy ◽  
U. Kaufmann
Keyword(s):  
Continuous Function ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Problems ◽  
Bounded Domains ◽  
Smooth Bounded Domain ◽  
Unbounded Function

AbstractLet Ω be a smooth bounded domain in RN and let m be a possibly discontinuous and unbounded function that changes sign in Ω. Let f : [0,∞) → [0,∞) be a nondecreasing continuous function such that k

Nonlinear elliptic problems on singularly perturbed domains

2001 ◽  
Vol 131 (5) ◽  
pp. 1023-1037 ◽  
Author(s):  
Jaeyoung Byeon
Keyword(s):  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Elliptic Problems ◽  
Singularly Perturbed ◽  
Bounded Domains ◽  
Nonlinear Elliptic Problem ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic

We consider how the shape of a domain affects the number of positive solutions of a nonlinear elliptic problem. In fact, we show that if a bounded domain Ω is sufficiently close to a union of disjoint bounded domains Ω1,…, Ωm, the number of positive solutions of a nonlinear elliptic problem on Ω is at least 2m −1.

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