Three positive solutions of semilinear elliptic equations in exterior cylinder domains

Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

Numerical approximation of axisymmetric positive solutions of semilinear elliptic equations in axisymmetric domains of R3

— We propose an algorithm which approaches positive solutions of elliptic semiliear equat boundary. n é ions with suhcritical nonlinearity in axisymmetric domains of M, with a degenerate

Positive Super-solutions to Semi-linear Second-order Non-divergence Type Elliptic Equations in Exterior Domains

We study the problem of the existence and non-existence of positive super-solutions to a semi-linear second-order non-divergence type elliptic equation ∑N i,j=1 aij(x) ∂2u ∂xi∂xj + up = 0, −∞ < p < ∞, with measurable coefficients in exterior domains of RN . We prove that in a “generic” situation there is one critical value of p that separates the existence region from nonexistence. We reveal th...

Minimal positive solutions for systems of semilinear elliptic equations

The paper is devoted to a system of semilinear PDEs containing gradient terms. Applying the approach based on Sattinger’s iteration procedure we use sub and supersolutions methods to prove the existence of positive solutions with minimal growth. These results can be applied for both sublinear and superlinear problems.

Symmetry-Breaking for Positive Solutions of Semilinear Elliptic Equations

In a recent interesting paper, GIDAS, NI, and NIRENBERG [2] proved that positive solutions of the Dirichlet problem for second-order semi-linear elliptic equations on balls must themselves be spherically symmetric functions. Here we consider the bifurcation problem for such solutions. Specifically, we investigate the ways in which the symmetric solution can bifurcate into a nonsymmetric solutio...