00-151 P.Amster, M.C. Mariani

Nonlinear two-point boundary value problems and a Duffing equation (23K, TEX) Apr 4, 00

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Abstract. In this paper we study a general semilinear second order ODE $$(pu')'+g(t,u,u') = f \tag{*}$$ Under an appropiate growth condition on $g$ we prove that the Dirichlet problem for (*) is uniquely solvable. Moreover, the set of $H^2$-solutions of (*) is homeomorphic to the two-dimensional real space. We also establish conditions for the existence of periodic solutions of (*).

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