Abstract.
In this paper we consider the problem \(-\Delta u + a(x)u = \vert u\vert ^{p-2}u\) in \(\mathbb{R}^N\), where p > 2 and \(p < 2^* = \frac{2N}{N-2} \) if N > 2. Assuming that the potential a(x) is a regular function such that \(\liminf_{\vert x\vert\rightarrow + \infty} a(x) = a_\infty > 0\) and that verifies suitable decay assumptions, but not requiring any symmetry property on it, we prove that the problem has infinitely many solutions.
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Received: 3 December 2003, Accepted: 10 May 2004, Published online: 22 December 2004
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Cerami, G., Devillanova, G. & Solimini, S. Infinitely many bound states for some nonlinear scalar field equations. Calc. Var. 23, 139–168 (2005). https://doi.org/10.1007/s00526-004-0293-6
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DOI: https://doi.org/10.1007/s00526-004-0293-6