Kandemir, MustafaMukhtarov, Oktay2022-03-162022-03-162017-01-12Kandemir, 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. 1-12.1072-6691https://hdl.handle.net/10877/15516We 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.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalSturm-Liouville problemnonlocal boundary conditionscoercivesolvabilityfredholmnessArticle