On the strong oscillatory behavior of all solutions to some second order evolution equations
Alain HarauxUniversité Pierre et Marie Curie, Paris, France
Let be any positive number. For any non-negative potential , we show that for any solution of in with on , and for any form , the function has a zero in each closed interval of with length . A similar result of uniform oscillation property on each interval of length at least equal to is established for all weak solutions of the equation in with on where is a nonnegative essentially bounded coefficient. These results apply in particular to any finite linear combination of evaluations of the solution at arbitrary points of .
Cite this article
Alain Haraux, On the strong oscillatory behavior of all solutions to some second order evolution equations. Port. Math. 72 (2015), no. 2/3, pp. 193–206DOI 10.4171/PM/1964