Uniqueness of positive solutions to a class of semilinear elliptic equations

Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

A remark on the uniqueness of positive solutions to semilinear elliptic equations with double power nonlinearities

We consider the uniqueness of positive solutions to

On Uniqueness of Boundary Blow-up Solutions of a Class of Nonlinear Elliptic Equations

We study boundary blow-up solutions of semilinear elliptic equations Lu = up + with p > 1, or Lu = e with a > 0, where L is a second order elliptic operator with measurable coefficients. Several uniqueness theorems and an existence theorem are obtained.

Existence, Uniqueness and Stability of Positive Solutions for a Class of Semilinear Elliptic Systems

We consider the stability of positive solutions to semilinear elliptic systems under a new general sublinear condition and its variants. Using the stability result and bifurcation theory, we prove the existence and uniqueness of positive solution and obtain the precise global bifurcation diagram of the system being a single monotone solution curve.