Summary
Let e be continuous and 2π-periodic, h continuous and bounded, and n>0 an integer. Sufficient conditions for the existence of 2π-periodic solutions of x″+n2x+h(x)= =e(t) are given. The proofs are based on a modification of Cesari's method and the Schauder fixed point theorem.
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Author is partially supported by N. S. F. under Grant 7447.
Entrata in Redazione il 26 agosto 1968.
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Lazer, A.C., Leach, D.E. Bounded perturbations of forced harmonic oscillators at resonance. Annali di Matematica 82, 49–68 (1969). https://doi.org/10.1007/BF02410787
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DOI: https://doi.org/10.1007/BF02410787