In this paper, we consider (n-1, 1)-type conjugate boundary value problem for the nonlinear fractional differential equation D0+u(t) + λf(t, u(t)) = 0, 0 < t < 1, λ > 0, u(0) = 0, 0 ≤ j ≤ n− 2, u(1) = 0, where λ is a parameter, α ∈ (n− 1, n] is a real number and n ≥ 3, and D0+ is the Riemann-Liouville’s fractional derivative, and f is continuous and semipositone. We give properties of Green’s f...

In this paper, we consider four-point coupled boundary value problem for systems of the nonlinear semipositone fractional differential equation

In this paper we present a novel variational approach to the question of existence and multiplicity of positive solutions to semipositone problems in a bounded smooth domain of RN . We consider both the sublinear and superlinear cases.

where λ is a positive parameter. The nonlinearity f(u) is called semipositone if f(0) < 0. In this paper we will only consider the positive solutions of (1.1). Semipositone problems were introduced by Castro and Shivaji in [CS1], and they arise from various disciplines, like astrophysics and population dynamics. (see [CMS] for more details.) It is possible that (1.1) has non-negative solutions ...

We prove the existence of positive solutions for a class semipositone problems with singular Trudinger-Moser nonlinearities. The proof is based on compactness and regularity arguments.

In this paper we prove the existence of positive solutions for a class of second order semipositone singular three-point boundary value problems. The results are obtained by the use of a GuoKrasnoselskii’s fixed point theorem in cones.

Keywords: Difference equations Boundary value problems Symmetric Green's function Fixed points Fourth-order Discrete Beam Lidstone Semipositone a b s t r a c t Various existence, multiplicity, and nonexistence results for nontrivial solutions to a non-linear discrete fourth-order Lidstone boundary value problem with dependence on two parameters are given, using a symmetric Green's function appr...

In this paper, we consider the existence of triple positive solutions for the second order semipositone m-point boundary value problem on time scales. We emphasize that the nonlinear term f may take a negative value.