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Singular periodic solutions for the p-laplacian ina punctured domain

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  • Abstract. In this paper we are interested in studying singular periodic solutions for the p-Laplacian in a punctured domain. We find an interesting phenomenon that there exists a critical exponent pc = N and a singular exponent qs = p-1. Precisely speaking, only if p > pc can singular periodic solutions exist; while if 1 < ppc then all of the solutions have no singularity. By the singular exponent qs = p-1, we mean that in the case when q = qs, completely different from the remaining case qqs, the problem may or may not have solutions depending on the coefficients of the equation.

    Mathematics Subject Classification: Primary: 35B10, 35K10; Secondary: 35K65.

    Citation:

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