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EXISTENCE THEOREMS FOR OPERATIONAL EQUATIONS
EXISTENCE THEOREMS FOR LIENARD SYSTEMS
EXISTENCE THEOREMS FOR ELLIPTIC PROBLEMS
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2ir-periodic a.e. t e arbitrary assumptions Banach space bifurcation equation boundary value problems bounded Cesari Ch.I compact consider constant continuous function COROLLARY defined denote differential equations Dirichlet problem dt dx eigenvalue equa equation Ex existence theorem F+(x Fatou's lemma fixed point index fixed point theorem follows given GPS u e GPS u e H greatest fixed point h e H Hilbert space hyperbolic implies inequality Kannan Lazer least one GPS LEMMA Leray-Schauder degree Let us assume lim sup linear operator Math MAWHIN method Moreover nonlinear problems nontrivial norm null space obtain ordinary differential equations periodic solutions priori estimate problems at resonance proof of Theorem prove resp satisfies second order selfadjoint solu solvability subset sufficient supersolution suppose t e G Theorem 2.i tion u e H zero