Publicación: A GENERAL RESULT TO THE EXISTENCE OF A PERIODIC SOLUTION TO AN INDEFINITE EQUATION WITH A WEAK SINGULARITY
Fecha
2019
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Journal of Dynamics and Differential Equations
Resumen
EFFICIENT CONDITIONS GUARANTEEING THE EXISTENCE OF A T - PERIODIC SOLUTION TO THE SECOND ORDER DIFFERENTIAL EQUATION U = H( T) U.,.. ( 0, 1), ARE ESTABLISHED. HERE, H. L( R/ TZ) IS A RATHER GENERAL SIGN- CHANGING FUNCTION WITH H < 0. IN CONTRAST WITH THE RESULTS IN GODOY AND ZAMORA ( PROC R SOC EDINB SECT A MATH) AND HAKL AND ZAMORA ( J DIFFER EQU 263: 451- 469, 2017), THE KEY INGREDIENT TO SOLVE THE AFOREMENTIONED PROBLEM SEEMS TO BE CONNECTED MORE WITH THE OSCILLATION AND THE SYMMETRY ASPECTS OF THE WEIGHT FUNCTION H THAN WITH THE MULTIPLICITY OF ITS ZEROES. ROUGHLY SPEAKING, THE SOLVABILITY FOR THE ABOVE- MENTIONED PROBLEM CAN BE GUARANTEED WHEN H+ H- AND H+ IS LARGE ENOUGH.
