We present a new min-max approach to the search of multiple T{periodic solutions to a class of fourth order equations u(iv)(t) cu"(t) = f(t, u(t)); t is an element of [0, T], where f( t; u) is continuous, T-periodic in t and satisfies a superlinearity assumption when \u\ --> infinity. For every n is an element of N, we prove the existence of a T{periodic solution having exactly 2n zeroes in (0, T].
Conti, M., Terracini, S., Verzini, G. (2004). Infinitely many solutions to fourth order superlinear periodic problems. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 356(8), 3283-3300 [10.1090/S0002-9947-03-03514-1].
Infinitely many solutions to fourth order superlinear periodic problems
TERRACINI, SUSANNA;
2004
Abstract
We present a new min-max approach to the search of multiple T{periodic solutions to a class of fourth order equations u(iv)(t) cu"(t) = f(t, u(t)); t is an element of [0, T], where f( t; u) is continuous, T-periodic in t and satisfies a superlinearity assumption when \u\ --> infinity. For every n is an element of N, we prove the existence of a T{periodic solution having exactly 2n zeroes in (0, T].
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