Concave Solutions of a Dirichlet Problem

Simultaneous Solutions of the Weak Dirichlet Problem

The main aim of this paper is a geometrical approach to simultaneous solutions of the abstract weak Dirichlet problem. We answer partially a question from the paper 2] where a similar problem was discussed from a potential-theoretical point of view for the case of function spaces consisting of harmonic functions.

Solutions of the Stochastic Dirichlet Problem

Wavelet Solutions for the Dirichlet Problem

A modiied classical penalty method for solving a Dirichlet boundary value problem is presented. This new ctitious domain/penalty method eliminates the traditional need of generating a complex computation grid in the case of irregular domain. It is based on the fact that one can expand the boundary measure under the chosen basis which leads to a fast, approximate calculation of boundary integral...

Two positive solutions of a quasilinear elliptic Dirichlet problem

For a class of second order quasilinear elliptic equations we establish the existence of two non-negative weak solutions of the Dirichlet problem on a bounded domain, Ω. Solutions of the boundary value problem are critical points of C−functional on H 0 (Ω). One solution is a local minimum and the other is of mountain pass type. Mathematics Subject Classification (2000). Primary 35J62; Secondary...

Radial Solutions to a Dirichlet Problem Involving Critical Exponents

In this paper we show that, for each λ > 0, the set of radially symmetric solutions to the boundary value problem −∆u(x) = λu(x) + u(x)|u(x)|, x ∈ B := {x ∈ R : ‖x‖ < 1}, u(x) = 0, x ∈ ∂B, is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.