In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Keywords: Positive solutions Cone Semipositone boundary value problems Infinite intervals a b s t r a c t By using the fixed...

We discuss the existence of positive solutions to −∆u = λf(u) in Ω, with u = 0 on the boundary, where λ is a positive parameter, Ω is a bounded domain with smooth boundary ∆ is the Laplacian operator, and f : (0,∞) → R is a continuous function. We first discuss the cases when f(0) > 0 (positone), f(0) = 0 and f(0) < 0 (semipositone). In particular, we will review the existence of non-negative s...

In this paper, multiple positive solutions for semipositone discrete eigenvalue problems are obtained by using a three critical points theorem for nondifferentiable functional. Keywords—Discrete eigenvalue problems, positive solutions, semipositone, three critical points theorem

Krasnoselskii’s fixed-point theorem in a cone is used to discuss the existence of positive solutions to semipositone conjugate and (n, p) problems. @ 2004 Elsevier Ltd. All rights reserved. Keywords-Existence, Positive solution, Semipositone, Conjugate and (n,p) problems.

We analyze the positive solutions to the singular boundary value problem −∆u = λ[f(u)− 1/u];x ∈ Ω u = 0; x ∈ ∂Ω, where f is a C function in (0,∞), f(0) ≥ 0, f ′ > 0, lims→∞ f(s) s = 0, λ is a positive parameter, α ∈ (0, 1) and Ω is a bounded region in R, n ≥ 1 with C boundary for some γ ∈ (0, 1). In the case n = 1 we use the quadrature method and for n > 1 we use the method of sub-super solutio...

In this paper, the existence, multiplicity and noexistence of positive solutions for a class of semipositone discrete boundary value problems with two parameters is studied by applying nonsmooth critical point theory and sub-super solutions method. Keywords—Discrete boundary value problems, nonsmooth critical point theory, positive solutions, semipositone, sub-super solutions method

We use the sub/supersolution method to analyze a semipositone Dirichlet problem for the p-Laplacian. To find a positive solution, we therefore focus on a related problem that produces positive subsolutions. We establish a new nonexistence result for this subsolution problem on general domains, discuss the existence of positive radial subsolutions on balls, and then apply our results to problems...

which arises in many different areas of applied mathematics and physics. Singular problems of this type that the nonlinearity g may change sign are referred to as singular semipositone problems in the literature. Motivated by BVP (1.1), this paper presents the existence results of the following second-order singular semipositone boundary value problem: { u ′′ + f(t, u) + g(t, u) = 0, 0 < t < 1,...

In this paper, we investigate the following third-order three-point semipositone boundary value problems: ( ) ( , ) 0, (0,1); (0) ( ) (1) 0, u t f t u t