Existence and multiplicity results for singular quasilinear elliptic equation on unbounded domain

2013 ◽  
Vol 37 (5) ◽  
pp. 768-779 ◽  
Author(s):  
Caisheng Chen ◽  
Lifang Shao
Keyword(s):  
Elliptic Equation ◽  
Unbounded Domain ◽  
Quasilinear Elliptic Equation ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic

Multiplicity results for a class of asymptotically p-linear equations on ℝN

2016 ◽  
Vol 18 (01) ◽  
pp. 1550031 ◽  
Author(s):  
Rossella Bartolo ◽  
Anna Maria Candela ◽  
Addolorata Salvatore
Keyword(s):  
Elliptic Equation ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Quasilinear Elliptic Equation ◽  
Linear Equations ◽  
Weighted Sobolev Spaces ◽  
Embedding Theorem ◽  
Multiplicity Results ◽  
Quasilinear Elliptic

The aim of this paper is investigating the multiplicity of weak solutions of the quasilinear elliptic equation [Formula: see text] in [Formula: see text], where [Formula: see text], the nonlinearity [Formula: see text] behaves as [Formula: see text] at infinity and [Formula: see text] is a potential satisfying suitable assumptions so that an embedding theorem for weighted Sobolev spaces holds. Both the non-resonant and resonant cases are analyzed.

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