scholarly journals Existence and multiplicity results for some quasilinear elliptic equation with weights

2008 ◽  
Vol 339 (2) ◽  
pp. 1084-1102 ◽  
Author(s):  
Leonelo Iturriaga
Keyword(s):  
Elliptic Equation ◽  
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.

scholarly journals Eigenvalue problems for a quasilinear elliptic equation onℝN

2005 ◽  
Vol 2005 (18) ◽  
pp. 2871-2882 ◽  
Author(s):  
Marilena N. Poulou ◽  
Nikolaos M. Stavrakakis
Keyword(s):  
Elliptic Equation ◽  
Weight Function ◽  
Quasilinear Elliptic Equation ◽  
Eigenvalue Problems ◽  
Principal Eigenvalue ◽  
Laplacian Operator ◽  
Quasilinear Elliptic

We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation−Δpu=λg(x)|u|p−2u,x∈ℝN,lim|x|→+∞u(x)=0, whereΔpu=div(|∇u|p−2∇u)is thep-Laplacian operator and the weight functiong(x), being bounded, changes sign and is negative and away from zero at infinity.

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