𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Spectral characteristics of some nonlocal boundary-value problems

✍ Scribed by E. Moiseev

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
304 KB
Volume
34
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

We consider two problems on eigenvalues of a nonlocal boundary-value problem for Laplace operator over a two-dimensional disk. We write out the adjoint boundary-value problems and show these problems have only eigenfunctions, but no associated functions. We also show that the spectrum of these problems does not lie in the Carleman parabola and the system of eigenfunctions, although complete and minimal in L2 is not a basis in L2. It is proved that, under certain assumptions a given function can be expanded into a biorthogonal series in the eigenfunctions of these problems, the series is uniformly convergent.

📜 SIMILAR VOLUMES

Existence Results for Some n-Dimensional
Existence Results for Some n-Dimensional Nonlocal Boundary Value Problems
✍ G.L. Karakostas; P.Ch. Tsamatos 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 82 KB

In this article, we study an nth dimensional nonlocal boundary value problem for a second order differential equation of Sturm᎐Liouville type. By using the linear part of the boundary condition an equivalent integral equation is obtained and then the nonlinear alternative fixed point result is appli

Second order nonlocal boundary value pro
Second order nonlocal boundary value problems at resonance
✍ Daniel Franco; Gennaro Infante; Mirosława Zima 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 110 KB

We present sufficient conditions for the existence of positive solutions for some second order boundary value problems at resonance. The boundary conditions that we study are quite general, involve a Stieltjes integral and include, as particular cases, multi-point and integral boundary conditions. O

Nonlocal boundary value problems for the
Nonlocal boundary value problems for the Schrödinger equation
✍ Allaberen Ashyralyev; Ali Sirma 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 273 KB

In the present paper, the nonlocal boundary value problem Schrödinger equation in a Hilbert space H with the self-adjoint operator A is considered. Stability estimates for the solution of this problem are established. Two nonlocal boundary value problems are investigated. The first and second order

Quasi-linear boundary value problems wit
Quasi-linear boundary value problems with generalized nonlocal boundary conditions
✍ Alejandro Vélez-Santiago 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 371 KB

We investigate a quasi-linear boundary value problem of the form -div(α|∇u| p-2 ∇u) = 0 involving a general boundary map and mixed Neumann boundary conditions on a bounded Lipschitz domain. We show existence, uniqueness, and Hölder continuity of the weak solution of this mixed boundary value problem