Topological Derivatives for Semilinear Elliptic Equations

The Nehari Manifold for a Class of Indefinite Weight 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.

Locating the peaks of semilinear elliptic systems

We consider a system of weakly coupled singularly perturbed semilinear elliptic equations. First, we obtain a Lipschitz regularity result for the associated ground energy function Σ as well as representation formulas for the left and the right derivatives. Then, we show that the concentration points of the solutions locate close to the critical points of Σ in the sense of subdifferential calcul...

Bifurcation Method for Solving Positive Solutions to a Class of Semilinear Elliptic Equations and Stability Analysis of Solutions

Semilinear elliptic equations are ubiquitous in natural sciences. They give rise to a variety of important phenomena in quantum mechanics, nonlinear optics, astrophysics, etc because they have rich multiple solutions. But the nontrivial solutions of semilinear equations are hard to be solved for the lack of stabilities, such as Lane-Emden equation, Henon equation and Chandrasekhar equation. In ...

Sharp Estimates for Semi-stable Radial Solutions of Semilinear Elliptic Equations

This paper is devoted to the study of semi-stable radial solutions u ∈ H1(B1) of −∆u = g(u) in B1 \ {0}, where g ∈ C (R) is a general nonlinearity and B1 is the unit ball of R N . We establish sharp pointwise estimates for such solutions. As an application of these results, we obtain optimal pointwise estimates for the extremal solution and its derivatives (up to order three) of the semilinear ...