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Existence of square integrable solutions of perturbed nonlinear differential equations

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


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