Symmetry classification and joint invariants for the scalar linear (1+1) elliptic equation

2015 ◽  
Vol 25 (1-3) ◽  
pp. 84-93 ◽  
Author(s):  
F.M. Mahomed ◽  
A.G. Johnpillai ◽  
A. Aslam
Keyword(s):  
Elliptic Equation ◽  
Symmetry Classification ◽  
Joint Invariants

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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