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Existence of square integrable solutions of perturbed nonlinear differential equations

Pages: 647 - 655, Issue Special, July 2003

 Abstract        Full Text (181.8K)              

Octavian G. Mustafa - Centre for Nonlinear Analysis, University of Craiova, Romania (email)
Yuri V. Rogovchenko - Department of Mathematics, Eastern Mediterranean University, Famagusta, TRNC, Mersin 10, Turkey (email)

Abstract: We give constructive proof of the existence of square integrable solutions for a class of $n$-th order nonlinear differential equations and discuss properties of square integrable solutions, obtaining as by-products an efficient estimate for the rate of decay of the $L^2$ norm of the solution and the nonexistence result due to Grammatikopoulos and Kulenovic [On the nonexistence of $L^2$-solutions of $n$-th order differential equations, Proc. Edinburgh Math. Soc. (2) 24 (1981), 131–136].

Keywords:  Nonlinear differential equations, square integrable solutions, existence, perturbation.
Mathematics Subject Classification:  34A12, 34C11, 34D10.

Received: August 2002;      Revised: March 2003;      Published: April 2003.