Existence and nonexistence results for critical growth polyharmonic elliptic systems

Existence and Nonexistence Results for Classes of Singular Elliptic Problem

and Applied Analysis 3 2. Proof of Theorems Consider the more general semilinear elliptic problem −Δu f x, u , in Ω, u > 0, in Ω, u 0, on ∂Ω, 2.1 where the function f x, s is locally Hölder continuous in Ω × 0,∞ and continuously differentiable with respect to the variable s. A function u is called to be a subsolution of problem 2.1 if u ∈ C2 Ω ∩ C Ω , and −Δu ≤ fx, u, in Ω, u > 0, in Ω, u 0, on...

Existence and Nonexistence Results for a Class of Quasilinear Elliptic Systems

A critical elliptic problem for polyharmonic operators

In this paper, we study the existence of solutions for a critical elliptic problem for polyharmonic operators. We prove the existence result in some general domain by minimizing on some infinite-dimensional Finsler manifold for some suitable perturbation of the critical nonlinearity when the dimension of domain is larger than critical one. For the critical dimensions, we prove also the existenc...

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 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...