Some oscillation criteria for the second order semilinear elliptic differential equation

A priori estimates for semilinear higher order elliptic equations usually have to deal with the absence of a maximum principle. This note presents some regularity polyharmonic Dirichlet problem that will make distinction between influence on solution positive and negative part right-hand side.

The paper studies the solution stability of a parametric control problem governed by semilinear elliptic equations with mixed state-control constraint, where objective function is nonconvex and admissible set unbounded. We show that under certain conditions, upper semicontinuous continuous respect to parameters.

We show that positive solutions of a semilinear elliptic problem in the Sobolev critical exponent with Newmann conditions, related to conformal deformation of metrics inR+, are asymptotically symmetric in a neighborhood of the origin. As a consequence, we prove for a related problem of conformal deformation of metrics in R+ that if a solution satisfies a Kazdan-Warner-type identity, then the co...

In this article, we deal with some problems involving a class of singularly perturbed elliptic operators. We prove the asymptotic preserving general Galerkin method associated to semilinear problem. use particular approximation estimate convergence rate on whole domain, for linear Finally, study behaviour semigroup generated.

Some oscillation criteria for the second order semilinear elliptic differential 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 ...

We show uniqueness results for the anisotropic Calder\'{o}n problem stated on transversally manifolds. Moreover, we give a convexity result range of Dirichlet-to-Neumann maps general Riemannian manifolds near zero potential. Finally, present type inverse problems associated to semilinear elliptic equations