Positive Solutions for Singular Semipositone Fractional Differential Equation Subject to Multipoint Boundary Conditions

Abstract

Existence result together with multiplicity result of positive solutions of higher-order fractional multipoint boundary value problems is given by considering the integrations of height functions on some special bounded sets. The nonlinearity may change its sign and may possess singularities on the time and the space variables at the same time.

Positive Solutions for a System of Hadamard-Type Fractional Differential Equations with Semipositone Nonlinearities

“…where α ∈ (2,3], D α is the Hadamard fractional derivative of order α, δ t(d/dt) (i.e., if u is ξ or η, then δu(t) t(d/dt)u(t); δu(1) lim t⟶1 + t(d/dt)u(t) (t(d/dt) u(t)| t 1 ) etc. ), and the nonlinearities f i (i 1, 2) satisfy the semipositone condition: (H0) f i ∈ C( [1, e] × R 6 + , R), and there exists M > 0 such that 6 + ,…”

Multiple positive solutions to singular fractional differential equations with integral boundary conditions involving $p-q$-order derivatives

“…As is well known, semipositone problems arise in bulking of mechanical systems, chemical reactions, astrophysics, combustion, management of natural resources, etc. Details are available in the works [2,6,15,21,23,24,26,29,32,34,35,37,39]. Studying positive solutions for semipositone problems is more difficult than that for positive problems.…”

Positive Solutions for a Hadamard Fractional p-Laplacian Three-Point Boundary Value Problem

“…where D α 0+ denotes the Riemann-Liouville fractional derivative. Positive solutions [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and nontrivial solutions [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] were also studied for fractional-order equations. For example, the authors in [16] used the Guo-Krasnoselskii's fixed-point theorem and the Leggett-Williams fixed-point theorem to study the existence and multiplicity of positive solutions for the fractional boundary-value problem…”