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Rendiconti Dell'Istituto Di Matematica Dell'Università Di Trieste


We are concerned with multiplicity and bifurcation results for solutions of nonlinear second order differential equations with general linear part and periodic boundary conditions. We impose asymptotic conditions on the nonlinearity and let the parameter vary. We then proceed to establish a priori estimates and prove multiplicity results (for large-norm solutions) when the parameter belongs to a (nontrivial) continuum of real numbers. Our results extend and complement those in the literature. The proofs are based on degree theory, continuation methods, and bifurcation from infinity techniques.


Nonlinear periodic bvp, maximum principles, principal eigenvalue, resonance, multiplicity, bifurcation from infinity, oscillatory conditions, a-priori estimates

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