Leonid KRITSKOV, Makhmud SADYBEKOV, Abdizhahan SARSENBI

176165

Properties in $L_p$ of root functions for a nonlocal problem with involution

The spectral problem $-u''(x)+\alpha u''(-x)=\lambda u(x)$, $-1$%lt; $x$ < $1$, with nonlocal boundary conditions $u(-1)=\beta u(1)$, $u'(-1)=u'(1)$, is studied in the spaces $L_p(-1,1)$ for any $\alpha\in (-1,1)$ and $\beta\ne\pm 1$. It is proved that if $r=\sqrt{(1-\alpha)/(1+\alpha)}$ is irrational then the system of its eigenfunctions is complete and minimal in $L_p(-1,1)$ for any $p>1$, but does not form a basis. In the case of a rational value of $r$, the way of supplying this system with associated functions is specified to make all the root functions a basis in $L_p(-1,1)$.
Keywords:

ODE with involution nonlocal boundary-value problem, basicity, root functions,

PDF
Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
Arşiv
Sayıdaki Diğer Makaleler

On the starlikeness of p-valent functions

Nak Eun CHO, Janusz SOKÓŁ, Mamoru NUNOKAWA, Oh Sang KWON

Curves over Finite Fields and Permutations of the Form $x^k-gamma Tr(x)$

Nurdagül ANBAR

Enveloping algebras of color hom-Lie algebras

Sergei SILVESTROV, Abdoreza ARMAKAN, Mohammad Reza FARHADPOOR

Curves over Finite Fields and Permutations of the Form $x^k-\gamma \mathrm{Tr}(x)$

Nurdagül Anbar MEIDL

Mohamed AMOUCH, Otmane BENCHIHEB

A Bernstein-type theorem for $\xi$-submanifolds with flat normal bundle in the Euclidean spaces

Xu-yong JİANG, He-jun SUN, PEIBIAO ZHAO

A novel 3-pass identification scheme and signature scheme based on multivariate quadratic polynomials

Sedat AKLEYLEK, Meryem SOYSALDI

Eta quotients of level 12 and weight 1

Ayşe ALACA, Şaban ALACA, Zafer Selçuk TUNCER

MELTEM SERTBAŞ, FATİH YILMAZ

Separation axioms on neutrosophic soft topological spaces

Sadi BAYRAMOV, Taha Yasin ÖZTÜRK, Çigdem GÜNÜUZ ARAS