Non-existence of positive solutions of some elliptic equations in positive-type domains

Non-existence of Positive Solutions of Fully Nonlinear Elliptic Equations in Unbounded Domains

In this paper we consider fully nonlinear elliptic operators of the form F (x, u,Du,D2u). Our aim is to prove that, under suitable assumptions on F , the only nonnegative viscosity super-solution u of F (x, u,Du,D2u) = 0 in an unbounded domain Ω is u ≡ 0. We show that this uniqueness result holds for the class of nonnegative super-solutions u satisfying inf x∈Ω u(x) + 1 dist(x, ∂Ω) = 0, and the...

Positive Super-solutions to Semi-linear Second-order Non-divergence Type Elliptic Equations in Exterior Domains

We study the problem of the existence and non-existence of positive super-solutions to a semi-linear second-order non-divergence type elliptic equation ∑N i,j=1 aij(x) ∂2u ∂xi∂xj + up = 0, −∞ < p < ∞, with measurable coefficients in exterior domains of RN . We prove that in a “generic” situation there is one critical value of p that separates the existence region from nonexistence. We reveal th...

EXISTENCE OF POSITIVE SOLUTIONS FOR SOME NONLINEAR ELLIPTIC PROBLEMS IN UNBOUNDED DOMAINS OF Rn

This paper deals with a class of nonlinear elliptic equations in an unbounded domain D of Rn, n≥ 3, with a nonempty compact boundary, where the nonlinear term satisfies some appropriate conditions related to a certain Kato class K∞(D). Our purpose is to give some existence results and asymptotic behaviour for positive solutions by using the Green function approach and the Schauder fixed point t...

Existence of Positive Radial Solutions for Some Nonlinear Elliptic Systems

In this paper we study a class of nonvariational elliptic systems, by using the Gidas-Spruck Blow-up method. first, we obtain a priori estimates, and then using Leray-Schauder topological degree theory, we establish the existence of positive radial solutions vanishing at infinity.

Existence of positive solutions of some semilinear elliptic equations with singular coefficients