Nonlinear elliptic equations with critical Sobolev exponent in nearly starshaped domains

2002 ◽  
Vol 335 (12) ◽  
pp. 1029-1032 ◽  
Author(s):  
Riccardo Molle ◽  
Donato Passaseo
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Critical Sobolev Exponent ◽  
Nonlinear Elliptic ◽  
Sobolev Exponent

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.

Positive solutions of nonlinear elliptic equations with critical Sobolev exponent and mixed boundary conditions

1990 ◽  
Vol 116 (1-2) ◽  
pp. 23-43 ◽  
Author(s):  
Massimo Grossi ◽  
Filomena Pacella
Keyword(s):  
Positive Solutions ◽  
Mixed Boundary ◽  
Nonlinear Elliptic Equations ◽  
Mixed Boundary Conditions ◽  
Critical Sobolev Exponent ◽  
Neumann Condition ◽  
Nonlinear Elliptic ◽  
Palais Smale Condition ◽  
Mixed Boundary Problem ◽  
Sobolev Exponent

SynopsisIn this paper we characterise the levels of the functional (0.3) at which the Palais-Smale condition fails in the Sobolev space V(Ω) defined below. From this result we deduce an existence theorem for positive solutions to the mixed boundary problem (0.1)–(0.2) under geometrical assumptions on the domain Ω and the part of the boundary of Ω where a Neumann condition is prescribed.

Sign in / Sign up

Export Citation Format

Share Document