In a previous paper [10], the author studied asymptotic behavior of coexistence steady-states to Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend infinity at same rate. As result, he proved that can be characterized by limiting system consists semilinear elliptic equation and an integral constraint. This studies set solutions system. The first main result gives suffic...

In this paper, we study the asymptotic behavior as x1 → +∞ of solutions of semilinear elliptic equations in quarteror half-spaces, for which the value at x1 = 0 is given. We prove the uniqueness and characterize the one-dimensional or constant profile of the solutions at infinity. To do so, we use two different approaches. The first one is a pure PDE approach and it is based on the maximum prin...

Abstract In this paper we deal with positive singular solutions to semilinear elliptic problems involving a first-order term and nonlinearity. Exploiting fine adaptation of the well-known moving plane method Alexandrov–Serrin careful choice cutoff functions, deduce symmetry monotonicity properties solutions.

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.