scholarly journals Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent

1991 ◽  
Vol 8 (2) ◽  
pp. 159-174 ◽  
Author(s):  
Zheng-Chao Han
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Critical Sobolev Exponent ◽  
Singular Solutions ◽  
Asymptotic Approach ◽  
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 ◽  
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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.

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