Multiplicity Results for a Semilinear, Elliptic Differential Equation with Conflicting Nonlinearities

Semilinear Elliptic Equations with Generalized Cubic Nonlinearities

A semilinear elliptic equation with generalized cubic nonlinearity is studied. Global bifurcation diagrams and the existence of multiple solutions are obtained and in certain cases, exact multiplicity is proved.

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.

Oscillation Theory for Semilinear Elliptic Equations with Arbitrary Nonlinearities

A two-phase free boundary problem for a semilinear elliptic equation

In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary‎. ‎We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...

Semilinear Elliptic Systems With Exponential Nonlinearities in Two Dimensions ∗

We establish a priori bounds for positive solutions of semilinear elliptic systems of the form 8><>>>: −∆u = g(x, v) , in Ω −∆v = f(x, u) , in Ω u > 0 , v > 0 in Ω