Displaying similar documents to “Weak solution for nonlinear degenerate elliptic problem with Dirichlet-type boundary condition in weighted Sobolev spaces”

Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket

Gabriele Bonanno, Giovanni Molica Bisci, Vicenţiu Rădulescu (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.

L²-data Dirichlet problem for weighted form Laplacians

Wojciech Kozłowski (2008)

Colloquium Mathematicae

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We solve the L²-data Dirichlet boundary problem for a weighted form Laplacian in the unit Euclidean ball. The solution is given explicitly as a sum of four series.