ON A FIRST-ORDER SEMIPOSITONE BOUNDARY VALUE PROBLEM ON A TIME SCALE

Applicable Analysis and Discrete Mathematics

article

Christopher S. Goodrich¹ 

[1] Department of Mathematics, Creighton Preparatory School

关键词: Time scales;    integral boundary condition;    first-order boundary value prob- lem;    cone;    positive solution;   

DOI  :  10.2298/AADM140812013G

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

We consider the existence of a positive solution to the first-order dynamicequation y∆(t)+p(t)yσ(t) = λf (t, yσ(t)) , t ∈ (a, b)T, subject to the boundarycondition y(a) = y(b) + R τ2τ1F(s, y(s)) ∆s for τ1, τ2 ∈ [a, b]T. In this setting,we allow f to take negative values for some (t, y). Our results generalize somerecent results for this class of problems, and because we treat the problemon a general time scale T we provide new results for this problem in the caseof differential, difference, and q-difference equations. We also provide somediscussion of the applicability of our results.

【 授权许可】

Unknown