Abstract
We find infinitely many solutions close to zero of the quasilinear elliptic equation \(-div\big (\phi (|\nabla u|^2)\nabla u\big )=f(x,u)\) in \(\Omega\) with Dirichlet’s boundary condition, where \(\Omega\) is a smooth bounded domain in \({\mathbb {R}}^N\), \(N\ge 1\) and \(f:\Omega \times {\mathbb {R}} \rightarrow {\mathbb {R}}\) is an unbounded continuous function with oscillatory behavior near the origin.
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Communicated by Claudio Gorodski.
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de Araujo, A.L.A., Abreu, R.d.R. Infinitely many solutions of a quasilinear elliptic equation with nonlinearity oscillating close to zero. São Paulo J. Math. Sci. 15, 427–434 (2021). https://doi.org/10.1007/s40863-020-00206-z
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DOI: https://doi.org/10.1007/s40863-020-00206-z