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Radial solutions of Neumann problems involving mean extrinsic curvature and periodic nonlinearities. (English) Zbl 1262.35088
Summary: 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 \[ \nabla \cdot \left(\frac{\nabla v}{\sqrt{1 - |\nabla v|^2}} \right) = g(|x|,v) + h(|x|) \] has at least one radial solution when \(g(|x|,\cdot )\) has a periodic indefinite integral and \({\int_{\mathcal A} h(|x|)\,{\mathrm{d}}x = 0.}\) The proof is based upon the direct method of the calculus of variations, variational inequalities and degree theory.

MSC:
35J20 Variational methods for second-order elliptic equations
35J60 Nonlinear elliptic equations
35J93 Quasilinear elliptic equations with mean curvature operator
35J87 Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators
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