Sublinear Elliptic Equation on Fractal Domains

2011 ◽  
Vol 24 (2) ◽  
pp. 97-113 ◽  
Author(s):  
He Zhenya
Keyword(s):  
Elliptic Equation ◽  
Fractal Domains

INFINITELY MANY SOLUTIONS FOR THE DIRICHLET PROBLEM ON THE SIERPINSKI GASKET

2011 ◽  
Vol 09 (03) ◽  
pp. 235-248 ◽  
Author(s):  
BRIGITTE E. BRECKNER ◽  
VICENŢIU D. RĂDULESCU ◽  
CSABA VARGA
Keyword(s):  
Boundary Condition ◽  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Nonlinear Elliptic Equation ◽  
Dirichlet Boundary ◽  
Sierpinski Gasket ◽  
Infinitely Many Solutions ◽  
Sierpiński Gasket ◽  
Nonlinear Elliptic ◽  
Fractal Domains

We study the nonlinear elliptic equation Δu(x) + a(x)u(x) = g(x)f(u(x)) on the Sierpinski gasket and with zero Dirichlet boundary condition. By extending a method introduced by Faraci and Kristály in the framework of Sobolev spaces to the case of function spaces on fractal domains, we establish the existence of infinitely many weak solutions.

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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