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

Sequences of Weak Solutions for Non-Local Elliptic Problems with Dirichlet Boundary Condition

2014 ◽  
Vol 57 (3) ◽  
pp. 779-809 ◽  
Author(s):  
Giovanni Molica Bisci ◽  
Pasquale F. Pizzimenti
Keyword(s):  
Boundary Condition ◽  
Dirichlet Problem ◽  
Variational Methods ◽  
Weak Solutions ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Infinitely Many Solutions ◽  
Distinct Sequence ◽  
Non Local ◽  
Kirchhoff Type Problems

AbstractIn this paper the existence of infinitely many solutions for a class of Kirchhoff-type problems involving the p-Laplacian, with p > 1, is established. By using variational methods, we determine unbounded real intervals of parameters such that the problems treated admit either an unbounded sequence of weak solutions, provided that the nonlinearity has a suitable behaviour at ∞, or a pairwise distinct sequence of weak solutions that strongly converges to 0 if a similar behaviour occurs at 0. Some comparisons with several results in the literature are pointed out. The last part of the work is devoted to the autonomous elliptic Dirichlet problem.

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