Publicación: ON THE POSITIVE PERIODIC SOLUTIONS OF A CLASS OF LIÉNARD EQUATIONS WITH REPULSIVE SINGULARITIES IN DEGENERATE CASE
Fecha
2023
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JOURNAL OF DIFFERENTIAL EQUATIONS
Resumen
IN THIS PAPER, WE STUDY THE EXISTENCE, MULTIPLICITY AND DYNAMICS OF POSITIVE PERIODIC SOLUTIONS TO A GENERALIZED LIÉNARD EQUATION WITH REPULSIVE SINGULARITIES. THE AMBROSETTI-PRODI TYPE RESULT IS PROVED IN THE ABSENCE OF THE SO-CALLED ANTICOERCIVITY CONDITION. FURTHERMORE, WITH S AS A PARAMETER, UNDER SOME CONDITIONS ON THE FUNCTION H, IT HAS BEEN SHOWN THAT FOR ANY M > 1 THERE EXISTS SM ? R SUCH THAT THE EQUATION X?? + F (X)X? + H(T, X) = S HAS TWO POSITIVE T -PERIODIC SOLUTIONS U1(·; S) AND U2(·; S) SATISFYING MIN{U1(T; S) : T ? [0, T ]} > M AND MIN{U2(T; S) : T ? [0, T ]} < 1/M FOR EVERY S < S M . AS A BY-PRODUCT OF THE PROPERTY, WE OBTAIN SUFFICIENT CONDITIONS TO GUARANTEE THE EXISTENCE OF POSITIVE T -PERIODIC SOLUTIONS OF INDEFINITE DIFFERENTIAL EQUATIONS.
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Repulsive singularity, Periodic solution, Liénard equation, Degree theory
