**InternationaleJournals**

**PERTURBATION RESULTS OF SPECTRUM OF STURM-LIOUVILLE DIFFERENTIAL OPERATORS**

**S. M. Padhye and K. J. Shinde**

Department of Mathematics, Shri RLT College of Science, Akola(MS) India.

Department of Mathematics, CAET, Dr. Panjabrao Deshmukh Krishi Vidyapeeth, Akola.

**ABSTRACT
**

Perturbation results of spectrum of Sturm-Liouville Differential Operators τu(x) = −u′′ (x) + q(x)u(x) defined on (a, b) are obtained. In particular suppose T is a maximal differential operator associated with differential expression τu(x) = −u′′ (x) + q(x)u(x) on L^{2}(a, b) and T_{n} is a maximal differential operator associated with differential expression τ_{n}u = −u′′ (x) + q_{n}(x)u(x) . We determine the sufficient conditions on q and q_{n} to get σ(T_{n}) → σ(T) and σe (T_{n})_{ }→ σe(T) . Here σ(T) denotes the spectrum of an operator T and σe(T) denotes the essential spectrum of an operator T.

**International
eJournal of Mathematical Sciences, Technology and Humanities**

**Volume** **3**,
**Issue** **2**, **Pages**: ** **973 - 977