We present some new existence results for singular positone and semipositone nonlinear fractional boundary value problemD0 u t μa t f t, u t , 0 < t < 1, u 0 u 1 u ′ 0 u′ 1 0, where μ > 0, a, and f are continuous, α ∈ 3, 4 is a real number, and D0 is Riemann-Liouville fractional derivative. Throughout our nonlinearity may be singular in its dependent variable. Two examples are also given to ill...

Using a numerical method based on sub-super solution, we will obtain positive solution to the coupled-system of boundary value problems of the form −∆u(x) = λf(x, u, v) x ∈ Ω −∆v(x) = λg(x, u, v) x ∈ Ω u(x) = 0 = v(x) x ∈ ∂Ω where f , g are C functions with at least one of f(x0, 0, 0) or g(x0, 0, 0) being negative for some x0 ∈ Ω (semipositone).

We prove the existence of positive solutions of the Sturm-Liouville boundary value problem −(r(t)φ(u′))′ = λg(t)f(t, u), t ∈ (0, 1), au(0)− bφ−1(r(0))u′(0) = 0, cu(1) + dφ−1(r(1))u′(1) = 0, where φ(u′) = |u′|p−2u′, p > 1, f : (0, 1) × (0,∞) → R satisfies a p-sublinear condition and is allowed to be singular at u = 0 with semipositone structure. Our results extend previously known results in the...

This paper studies the existence of positive solutions for a class of second-order semipositone differential equations with a negatively perturbed term and integral boundary conditions. By using a well-known fixed-point index theorem, some new existence results are derived for the case where nonlinearity is allowed to be sign changing. Several examples are presented to demonstrate the applicati...

This study concerns the existence of positive solutions to classes of boundary value problems of the form where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in R N (N ≥ 2) with ∂Ω of class C 2 , and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x, u).

We consider the boundary value problem −∆pu = λ f (u) in Ω satisfying u = 0 on ∂Ω, where u= 0 on ∂Ω, λ > 0 is a parameter, Ω is a bounded domain in Rn with C2 boundary ∂Ω, and ∆pu := div(|∇u|p−2∇u) for p > 1. Here, f : [0,r] → R is a C1 nondecreasing function for some r > 0 satisfying f (0) < 0 (semipositone). We establish a range of λ for which the above problem has a positive solution when f ...