Qualitative properties of solutions to elliptic singular problems

Accurate techniques for computing singular solutions of elliptic problems

Generalized functions occur in many practical applications as source terms in partial differential equations. Typical examples are point sources and sinks in porous media flow that are described by Dirac δ-functions or point loads and dipoles as source terms for electrostatic potentials. For analyzing the accuracy of such computations, standard techniques cannot be used, since they rely on glob...

Two weak solutions for some singular fourth order elliptic problems

In this paper, we establish the existence of at least two distinct weak solutions for some singular elliptic problems involving a p-biharmonic operator, subject to Navier boundary conditions in a smooth bounded domain in RN . A critical point result for differentiable functionals is exploited, in order to prove that the problem admits at least two distinct nontrivial weak solutions.

Singular Solutions for some Semilinear Elliptic Equations

We are concerned with the behavior of u near x = O. There are two distinct cases: 1) When p >= N / ( N -2) and (N ~ 3) it has been shown by BR~ZIS & V~RON [9] that u must be smooth at 0 (See also BARAS & PIERRE [1] for a different proof). In other words, isolated singularities are removable. 2) When 1-< p < N / ( N 2) there are solutions of (1) with a singularity at x ---0. Moreover all singula...

Explicit multiple singular periodic solutions and singular soliton solutions to KdV equation

 Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...

Asymptotic Solutions of Singular Perturbation Problems for Linear Differential Equations of Elliptic Type