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Amer Assume assumptions Banach space Birkhoff boundary value problem calculus of variations Caratheodory coincidence degree compact consider continuous convex COROLLARY critical points defined eigenfunctions eigenvalues EKELAND equation with damping equivalent fixed point follows Fourier series FUCIK Hamiltonian systems heat equation hence hold uniformly implies inequalities INSTITUT DE MATHEMATIQUE invariant J.R. WARD jumping nonlinearities least one GPS least one solution Lemma Leray-Schauder's lim inf lim sup linear operator MAWHIN Moreover Morse index Morse theory N(E+rI NKASHAMA nonlinear nonresonance conditions nonuniform nonresonance norm obtain ordinary differential equations paper parabolic equations Parseval equality periodic orbits periodic solutions Poincare Poincare's positive measure problem x"(t proof is complete proof of Theorem prove Rabinowitz Remark satisfies Schauder self-adjoint solutions of Hamiltonian solvability subsection 2.1 T-periodic Theorem 1.1 tion topological uniformly for a.e. WILLEM x"Ct x2Ct zero