R + →R is a sign-changing function. In recent years, positive solutions of boundary value problems for difference equations have been widely studied. See [–] and the references therein. However, little work has been done that has referred to the existence of positive solutions for discrete boundary value problems with sign-changing nonlinearities (see []). Usually, in order to obtain posit...

In this note we are mainly concerned with existence result for semilinear semipositone elliptic equation of the form ⎧⎨ ⎩ −Δu = λa(x)vα − c, x ∈ Ω, −Δv = λb(x)uβ − c, x ∈ Ω, u = v = 0, x ∈ ∂Ω, where Δ denote the Laplacian operator, Ω is a bounded domain in RN (N > 1) with ∂Ω of class C2, λ, c are positive parameters, α, β > 0 and the weight a(x), b(x) satisfying a(x) ∈ C(Ω), b(x) ∈ C(Ω) and a(x...

<p style='text-indent:20px;'>In this paper we prove the existence of at least one positive solution for nonlocal semipositone problem type</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ (P_\lambda^\mu)\left\{ \begin{array}{rcl} (-\Delta)^s u& = & \lambda(u^{q}-1)+\mu u^r \text{ in } \Omega\\ u&amp...

Correspondence: [email protected]. cn Department of Mathematics, Shanghai Normal University, Shanghai 200234, People’s Republic of China Abstract In this article, some new sufficient conditions are obtained by making use of fixed point index theory in cone and constructing some available integral operators together with approximating technique. They guarantee the existence of at least one positive ...