Existence of Positive Solutions for Semipositone Higher-Order BVPS on Time Scales | Zendy

Yuguo Lin | Zendy; Minghe Pei | Zendy

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Existence of Positive Solutions for Semipositone Higher-Order BVPS on Time Scales

Author(s) -

Yuguo Lin,

Minghe Pei

Publication year - 2010

Publication title -

advances in difference equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.67

H-Index - 51

eISSN - 1687-1847

pISSN - 1687-1839

DOI - 10.1155/2010/235296

Subject(s) - order (exchange) , mathematics , ordinary differential equation , partial differential equation , mathematical analysis , differential equation , economics , finance

We offer conditions on semipositone function f(t,u0,u1,…,un-2) such that the boundary value problem, uΔn(t)+f(t,u(σn-1(t)),uΔ(σn-2(t)),…,uΔn-2(σ(t)))=0, t∈(0,1)∩𝕋, n≥2, uΔi(0)=0, i=0,1,…,n-3, αuΔn-2(0)-βuΔn-1(0)=0, γuΔn-2(σ(1))+δuΔn-1(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,u0,u1,…,un-2)≥-M for some positive constant M

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