We consider the T-periodic problem [Formula omitted] where g: [Formula omitted] exhibits a singularity of a repulsive type at the origin, and an asymptotically linear behaviour at infinity. In particular, for large x, g(t, x) is controlled from both sides by two consecutive asymptotes of the T-periodic FuÄik spectrum, with possible equality on one side. Using a suitable Landesman-Lazer-type condition, we prove the existence of a solution. © 2012, Royal Society of Edinburgh. All rights reserved.
A Landesman---Lazer-type condition for asymptotically linear second-order equations with a singularity
Garrione, Maurizio
2012-01-01
Abstract
We consider the T-periodic problem [Formula omitted] where g: [Formula omitted] exhibits a singularity of a repulsive type at the origin, and an asymptotically linear behaviour at infinity. In particular, for large x, g(t, x) is controlled from both sides by two consecutive asymptotes of the T-periodic FuÄik spectrum, with possible equality on one side. Using a suitable Landesman-Lazer-type condition, we prove the existence of a solution. © 2012, Royal Society of Edinburgh. All rights reserved.File in questo prodotto:
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