DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS ON INFINITE INTERVAL

Authors

  • Hosein Ansari Azad University of Ahar, Iran

DOI:

https://doi.org/10.46991/PYSU:A/2011.45.2.027

Keywords:

Dirichlet problem, weighted Sobolev spaces, differential equations in abstract spaces, spectrum of the linear operator

Abstract

In the present paper we consider the Dirichlet problem for the fourth order differential-operator equation $Lu \equiv(t^{\alpha}u^{\prime\prime})^{\prime\prime}+t^{-2}Au = f$ , where $t\in(1, +\infty), \alpha\geq 2, f \in L_{2,2}((1, +\infty), H),~A$ is a linear operator in the separable Hilbert space H and has a complete system of eigenvectors that form a Riesz basis in H. The existence and uniqueness of the generalized solution for the Dirichlet problem are proved, and the description of spectrum for the corresponding operator is given.

Downloads

Published

2011-04-28

How to Cite

Ansari, H. (2011). DEGENERATE DIFFERENTIAL-OPERATOR EQUATIONS ON INFINITE INTERVAL. Proceedings of the YSU A: Physical and Mathematical Sciences, 45(2 (225), 27–32. https://doi.org/10.46991/PYSU:A/2011.45.2.027

Issue

Section

Mathematics