In this paper, we study the existence of positive solutions for a class of coupled integral boundary value problems of nonlinear semipositone Hadamard fractional differential equations Du(t) + λf(t, u(t), v(t)) = 0, Dv(t) + λg(t, u(t), v(t)) = 0, t ∈ (1, e), λ > 0, u(1) = v(1) = 0, 0 ≤ j ≤ n− 2, u(e) = μ ∫ e 1 v(s) ds s , v(e) = ν ∫ e

In this paper we use the method of upper and lower solutions combined with degree theoretic techniques to prove the existence of multiple positive solutions to semipositone superlinear systems of the form −∆u = g1(x, u, v) −∆v = g2(x, u, v) on a smooth, bounded domain Ω ⊂ R with Dirichlet boundary conditions, under suitable conditions on g1 and g2. Our techniques apply generally to subcritical,...

This paper investigates the existence of at least two positive solutions for the following high-order fractional semipositone boundary value problem (SBVP, for short) with coupled integral boundary value conditions:  D0+u(t) + λf(t,u(t), v(t)) = 0, t ∈ (0, 1), D0+v(t) + λg(t,u(t), v(t)) = 0, t ∈ (0, 1), u(j)(0) = v(j)(0) = 0, j = 0, 1, 2, · · · ,n− 2, Dα−1 0+ u(1) = λ1 ∫η1 0 v(t)...

We examine the existence and multiplicity of positive solutions for a class nonlinear semipositone fractional differential equations involving integral boundary conditions. The results are obtained in terms different intervals parameters by means Leray-Schauder Guo-Krasnoselskii fixed point theorems. Examples included to verify our main results.

We offer conditions on semipositone function f t, u0, u1, . . . , un−2 such that the boundary value problem, uΔ n t f t, u σn−1 t , uΔ σn−2 t , . . . , uΔ n−2 σ t 0, t ∈ 0, 1 ∩ T, n ≥ 2, uΔi 0 0, i 0, 1, . . . , n − 3, αuΔ 0 − βuΔ 0 0, γuΔ σ 1 δuΔ σ 1 0, has at least one positive solution, where T is a time scale and f t, u0, u1, . . . , un−2 ∈ C 0, 1 × R 0,∞ n−1,R −∞,∞ is continuous with f t, ...

In this paper, we are concerned with the existence of positive solution following semipositone boundary value problem on time scales: \begin{equation*} (\psi(t)y^\Delta (t))^\nabla + \lambda_1 g(t, \,y(t)) \lambda_2 h(t,\,y(t)) = 0, \,t \in [\rho(c), \,\sigma(d)]_\mathbb{T}, \end{equation*} mixed conditions \begin{split} \alpha y(\rho(c))-\beta \psi(\rho(c)) y^\Delta(\rho(c))=0,\\ \gamma y(\sig...

By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple positive solutions for the third-order three-point singular semipositone BVP: x ′′′ (t) − λ f (t, x) = 0, t ∈ (0, 1); x(0) = x ′ (η) = x ′′ (1) = 0, where 1 2 < η < 1, the non-linear term f (t, x): (0, 1) × (0, +∞) → (−∞, +∞) is continuous and may be singular at t = 0, t = 1...

Using the method of upper and lower solutions, we prove that the singular boundary value problem, −u = f(u) u in (0, 1), u(0) = 0 = u(1) , has a positive solution when 0 < α < 1 and f : R → R is an appropriate nonlinearity that is bounded below; in particular, we allow f to satisfy the semipositone condition f(0) < 0. The main difficulty of this approach is obtaining a positive subsolution, whi...