Existence of Strictly Positive Solutions for Sublinear Elliptic Problems in Bounded Domains

Abstract

Let Ω be a smooth bounded domain in RN and let m be a possibly discontinuous and unbounded function that changes sign in Ω. Let f : [0,∞) → [0,∞) be a nondecreasing continuous function such that k

Positivity results for indefinite sublinear elliptic problems via a continuity argument

“…[12]). In this sense, Corollaries 1.4 and 1.5 are consistent with the existence results from [12,13].…”

Strictly Positive Solutions for One-Dimensional Nonlinear Problems Involving the -Laplacian

“…We would like to conclude this introduction with some few words on the corresponding n-dimensional problem. As we noticed in the above paragraph the condition in [9] is still valid in this case, and some of the techniques in [6] can be applied if L = −∆ (see Section 3 in [6] for the radial case, and also [7]). We are strongly convinced that some of the theorems presented here should still have some counterpart in n dimensions but we are not able to provide a proof.…”

On Dirichlet problems with singular nonlinearity of indefinite sign

“…[15], [7], [18]), but to our knowledge no theorems are known when m is allowed to change sign in Ω. In fact, even when (1.2) is sublinear (that is, γ ∈ (−1, 0)) and one-dimensional, these kind of problems are quite intriguing and involved and, as far as we know, only recently existence of (strictly) positive solutions has started being studied in detail when m changes sign in Ω (see [13], [16], [14] and [10]; and [17] for the p-laplacian). Let us also mention that nonnegative solutions of these semilinear problems have been studied carefully in [2].…”