Nonlocal Sturm-Liouville problems with integral terms in the boundary conditions
Date
2017-01-12
Authors
Kandemir, Mustafa
Mukhtarov, Oktay
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider a new type Sturm-Liouville problems whose main feature is the nature of boundary conditions. Namely, we study the nonhomogeneous Sturm-Liouville equation.
p(x)u″(x) + (q(x) - λ)u = ƒ(x)
on two disjoint intervals [-1, 0) and (0, 1], subject to the nonlocal boundary-transmission conditions
αku(mk) (-1) + βku(mk) (-0) + ηku(mk) (+0) + γku(mk) (1)
+ ∑nkj=1 δkju(mk) (xkj) + ∑2v=1 ∑mkj=0 ∫ΩvK kvj(t)u(j) (t)dt = ƒk, k = 1, 2, 3, 4.
where Ω1 ≔ [-1, 0), Ω2 ≔ (0, 1] and x kj ∈ (-1, 0) ∪ (0, 1) are internal points. By using our own approaches we establish such important properties as Fredholmness, coercive solvability and isomorphism with respect to the spectral parameter λ.
Description
Keywords
Sturm-Liouville problem, nonlocal boundary conditions, coercive, solvability, fredholmness
Citation
Kandemir, M., & Mukhtarov, O. S. (2017). Nonlocal Sturm-Liouville problems with integral terms in the boundary conditions. <i>Electronic Journal of Differential Equations, 2017</i>(11), pp. 1-12.
Rights
Attribution 4.0 International