On the uniqueness of positive solution of an elliptic equation

Abstract

This work deals with the uniqueness of positive solution for an elliptic equation whose nonlinearity satisfies an specific monotony property. In order to prove the main result, we employ a change of variable used in previous papers and the maximum principle.

Positivity results for indefinite sublinear elliptic problems via a continuity argument

“…In particular, u ∈ P • D . Finally, by the assumptions on f and Theorem 2.1 in [10], we also know that there is at most one positive solution of (P ). Therefore there are no other nontrivial nonnegative solutions of (P ).…”

On strictly positive solutions for some semilinear elliptic problems

“…Let us mention that neither of these conditions are comparable with each other (see Remarks 2.2, 2.4 and 2.6). Let us also notice that the distinction between strictly positive solutions and solutions in the interior of the positive cone is of importance since the positive solution of (1.1), if it exists, is unique (see e.g., [9], Theorem 2.1). On the other hand, in Theorem 2.7 we shall exhibit necessary conditions for the existence of strictly positive solutions, which are of similar type as the ones stated in the above theorems.…”

Positive solutions of an elliptic Neumann problem with a sublinear indefinite nonlinearity

“…Indeed, this follows from either the fact that the sub and supersolutions can be chosen radial, or because the solution of (3.5) is unique (cf. [7]) and v (Sx) is also a solution if S is an isometry of R N . Furthermore, it is also easy to check that r → v(r) is nonincreasing in (0, R 0 ) because a ≥ 0 in B R0 .…”