INFINITELY MANY SOLUTIONS FOR A NONLINEAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV EXPONENT

1991 ◽  
Vol 11 (2) ◽  
pp. 128-135 ◽  
Author(s):  
Wenxiong Chen
Keyword(s):  
Elliptic Equation ◽  
Nonlinear Elliptic Equation ◽  
Critical Sobolev Exponent ◽  
Infinitely Many Solutions ◽  
Nonlinear Elliptic ◽  
Sobolev Exponent

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.

Multiplicity and Existence Results for a Nonlinear Elliptic Equation With Sobolev Exponent

2010 ◽  
Vol 10 (3) ◽  
Author(s):  
Zakaria Bouchech ◽  
Hichem Chtioui
Keyword(s):  
Elliptic Equation ◽  
Boundary Conditions ◽  
Nonlinear Elliptic Equation ◽  
Dirichlet Boundary ◽  
Existence Results ◽  
Dirichlet Boundary Conditions ◽  
Nonlinear Elliptic ◽  
Sobolev Exponent

AbstractIn this paper we consider the following nonlinear elliptic equation with Dirichlet boundary conditions: -Δu = K(x)u

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