Existence and non-existence results for fully nonlinear elliptic systems

Existence and non-existence results for fully nonlinear elliptic systems

We study systems of two elliptic equations, with right-hand sides with general power-like superlinear growth, and left-hand sides which are of Isaac’s or Hamilton-Jacobi-Bellman type (however our results are new even for linear lefthand sides). We show that under appropriate growth conditions such systems have positive solutions in bounded domains, and that all such solutions are bounded in the...

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

Existence Results for Strongly Indefinite Elliptic Systems

In this paper, we show the existence of solutions for the strongly indefinite elliptic system −∆u = λu+ f(x, v) in Ω, −∆v = λv + g(x, u) in Ω, u = v = 0, on ∂Ω, where Ω is a bounded domain in RN (N ≥ 3) with smooth boundary, λk0 < λ < λk0+1, where λk is the kth eigenvalue of −∆ in Ω with zero Dirichlet boundary condition. Both cases when f, g being superlinear and asymptotically linear at infin...

Existence and Comparison Results for Fully Nonlinear Degenerate Elliptic Equations without Zeroth-Order Term

Existence of strong solutions of fully nonlinear elliptic equations

The aim of this paper is to study the solvability of the Dirichlet problem for certain types of fully nonlinear elliptic equations. The theory of weakly-near operators, combined to Contraction Mapping and Schauder fixed point theorems, is used. Our main results generalizes similar ones given by S. Campanato and A. Tarsia.