On a class of semilinear elliptic systems

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.

Existence Results for a Class of Semilinear Degenerate Elliptic Equations

We prove existence results for the Dirichlet problem associated with an elliptic semilinear second-order equation of divergence form. Degeneracy in the ellipticity condition is allowed.

Symmetry Breaking for a Class of Semilinear Elliptic Problems

We study positive solutions of the Dirichlet problem for —Ají = up — A, p > 1, A > 0, on the unit ball 0. We show that there exists a positive solution (uo, Ao) of this problem which satisfies in addition duo/dn = 0 on âfî. We prove also that at (uo,Ao), the symmetry breaks, i.e. asymmetric solutions bifurcate from the positive radial solutions.

Existence of positive solutions of a class of semilinear elliptic systems

Abstract: By a compactness argument, it was shown that, the boundary regularity theorems of Schoen-Uhlenbeck [A regularity theory for harmonic maps. J. Differential Geom. 17 (1982), no. 2, 307–335] and Jost-Meier [Boundary regularity for minima of certain quadratic functionals. Math. Ann. 262 (1983), no. 4, 549–561] are uniform in the domains, boundary data, and the energy. The resulting estima...