Periodic boundary value problem in Hilbert space for differential equation of second order with reflection of the argument. (English) Zbl 0744.34062

Author’s abstract: “The differential equation \(-x''+a^ 2x+f(t,x(t),x(- t))=h(t)\) with periodic boundary conditions is studied. The existence of a solution in case when \(f\) is a completely continuous operator and in case when \(f\) is only continuous and bounded is proved. The connectedness of the set of solutions is studied”.
Reviewer: J.F.Toland (Bath)


34G20 Nonlinear differential equations in abstract spaces
34B15 Nonlinear boundary value problems for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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