Existence of positive solutions for a class of superlinear semipositone systems

On the existence of multiple positive solutions to some superlinear systems

“…We will give explicit conditions for the existence of the required ordered, strictly positive upper and lower solution pair. Our result is complementary to the existence and non-existence results of Chhetri and Girg [3]. Our theorem here also complements the single equation positone results in [12] and generalizes the single equation radially symmetric results in [20].…”

Existence of positive solutions for a semipositone p-Laplacian problem

“…Finally, using order properties of −∆ p , we prove that by further restricting λ such a solution is actually positive. For recent results on semipositone problems the reader is referred to [2,3]. …”

Existence of positive radial solutions for superlinear, semipositone problems on the exterior of a ball

“…Here, the reaction term f : [0, ∞) → R is a nondecreasing, C 1 function such that The case when f (0) < 0 is referred to in the literature as a semipositone problem, and it has been well documented (see [22], [6]) that they pose considerably more challenges in the study of positive solutions than the case where f (0) > 0 (positone problems). For a rich history of superlinear, semipositone problems on bounded domains with Dirichlet boundary conditions, see [2], [3], [4], [5], [7], [8], [10], [11], [12], [13], [14], [15], [16], [20], [21], and [26]. The main focus of this paper is to extend an important existence result for λ ≈ 0 obtained in the case of bounded domains with Dirichlet boundary conditions to a domain exterior to a ball, and also to problems involving classes of nonlinear boundary conditions on the boundary of the ball.…”