Abstract
We show that if \({{\mathcal A} \subset \mathbb{R}^N}\) is an annulus or a ball centered at zero, the homogeneous Neumann problem on \({{\mathcal A}}\) for the equation with continuous data
has at least one radial solution when g(|x|,·) has a periodic indefinite integral and \({\int_{\mathcal A} h(|x|)\,{\rm{d}}x = 0.}\) The proof is based upon the direct method of the calculus of variations, variational inequalities and degree theory.
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Communicated by A. Malchiodi.
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Bereanu, C., Jebelean, P. & Mawhin, J. Radial solutions of Neumann problems involving mean extrinsic curvature and periodic nonlinearities. Calc. Var. 46, 113–122 (2013). https://doi.org/10.1007/s00526-011-0476-x
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DOI: https://doi.org/10.1007/s00526-011-0476-x