Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems. (English) Zbl 1080.34532

Summary: We examine nonlinear periodic systems driven by the vectorial \(p\)-Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the “sublinear” problem. For the semilinear problem (i.e., \(p = 2\)) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem for the “superlinear” problem. Our work generalizes some recent results of C.-L. Tang [Proc. Am. Math. Soc. 126, 3263-3270 (1998; Zbl 0902.34036)].


34C25 Periodic solutions to ordinary differential equations


Zbl 0902.34036
Full Text: DOI EuDML


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