Abstract
In this paper, we study a discrete nonlinear boundary value problem that involves a nonlinear term oscillating near the origin and a power-type nonlinearity \(u^p\). By using variational methods, we establish the existence of a sequence of non-negative weak solutions that converges to 0 if \(p\ge 1\). In the sublinear case, we prove that for all n positive integer, the problem has at least n weak solutions if the parameter lies in a certain range.
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Dedicated with esteem to Professor Hugo Beirão da Veiga on his 70th anniversary.
V. Rădulescu acknowledges the support through the research grant CNCS-UEFISCDI-PCCA-43C/2014. V. Rădulescu would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Free Boundary Problems and Related Topics, where work on this paper was undertaken.
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Mălin, M., Rădulescu, V.D. Infinitely many solutions for a nonlinear difference equation with oscillatory nonlinearity. Ricerche mat. 65, 193–208 (2016). https://doi.org/10.1007/s11587-016-0260-5
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DOI: https://doi.org/10.1007/s11587-016-0260-5