EXISTENCE OF SQUARE INTEGRABLE SOLUTIONS OF PERTURBED NONLINEAR DIFFERENTIAL EQUATIONS

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].