NEUMANN PROBLEM FOR FOURTH ORDER DEGENERATE ORDINARY DIFFERENTIAL EQUATIONS

L. P. Tepoyan; Daryoush Kalvand

doi:10.46991/PYSU:A/2010.44.1.022

NEUMANN PROBLEM FOR FOURTH ORDER DEGENERATE ORDINARY DIFFERENTIAL EQUATIONS

Authors

L. P. Tepoyan Chair of Differential Equations, YSU, Armenia
Daryoush Kalvand Azad University of Karraj, Iran

DOI:

https://doi.org/10.46991/PYSU:A/2010.44.1.022

Keywords:

Neumann problem, weighted Sobolev spaces, generalized solution, spectrum of linear operators

Abstract

In the present paper the Neumann problem for the equation $Lu \equiv (t^\alpha u^\alpha)''+ au +f,$ where $0\leq \alpha\leq 4,~t\in[0, b],~f\in L_2(0, b)$ , is considered. Firstly, the weighted Sobolev space $W^2_\alpha$ and generalized solution for the abovementioned equation are defined. Then, the existence and uniqueness of the generalized solution is studied, as well as the spectrum and the domain of corresponding operator are described.

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Published

2010-01-26

How to Cite

Tepoyan, L. P., & Kalvand, D. (2010). NEUMANN PROBLEM FOR FOURTH ORDER DEGENERATE ORDINARY DIFFERENTIAL EQUATIONS. Proceedings of the YSU A: Physical and Mathematical Sciences, 44(1 (221), 22–26. https://doi.org/10.46991/PYSU:A/2010.44.1.022