American Institute of Mathematical Sciences

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2003, 2003(Special): 647-655. doi: 10.3934/proc.2003.2003.647

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, Romania
2. 

Department of Mathematics, Eastern Mediterranean University, Famagusta, TRNC, Mersin 10, Turkey

Received  August 2002 Revised  March 2003 Published  April 2003

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: perturbation., existence, Nonlinear differential equations, square integrable solutions.
Mathematics Subject Classification: 34A12, 34C11, 34D1.
Citation: Octavian G. Mustafa, Yuri V. Rogovchenko. Existence of square integrable solutions of perturbed nonlinear differential equations. Conference Publications, 2003, 2003 (Special) : 647-655. doi: 10.3934/proc.2003.2003.647
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