Existence of square integrable solutions of perturbed nonlinear differential equations

Octavian G. Mustafa; Yuri V. Rogovchenko

doi:10.3934/proc.2003.2003.647

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2003, Volume 2003: 647-655. Doi: 10.3934/proc.2003.2003.647 open access

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Existence of square integrable solutions of perturbed nonlinear differential equations

Octavian G. Mustafa^1, and
Yuri V. Rogovchenko^2,

1.
Centre for Nonlinear Analysis, University of Craiova
2.
Department of Mathematics, Eastern Mediterranean University, Famagusta, TRNC, Mersin 10

Received: July 31, 2002

Revised: February 28, 2003

Published: March 2003

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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].

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Mathematics Subject Classification: 34A12, 34C11, 34D10.

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