Radial solutions of Neumann problems involving mean extrinsic curvature and periodic nonlinearities

Bereanu, Cristian;Jebelean, Petru;Mawhin, Jean
(2013) Calculus of Variations and Partial Differential Equations — Vol. 46, n° 1-2, p. 113-122 (2013)

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Authors
  • Bereanu, CristianInstitute of Mathematics “Simion Stoilow”, Romanian Academy, Bucharest, Romania
    Author
  • Jebelean, PetruDepartment of Mathematics, West University of Timişoara, Timişoara, Romania
    Author
  • Mawhin, JeanUCLouvain
    Author
Abstract
We show that if A ⊂ ℝ<sup>N</sup> is an annulus or a ball centered at zero, the homogeneous Neumann problem on A for the equation with continuous data, has at least one radial solution when g({pipe}x{pipe},·) has a periodic indefinite integral and ∫<inf>A</inf>h({pipe}x{pipe})dx=0 The proof is based upon the direct method of the calculus of variations, variational inequalities and degree theory. © 2011 Springer-Verlag.
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Bereanu, C., Jebelean, P., & Mawhin, J. (2013). Radial solutions of Neumann problems involving mean extrinsic curvature and periodic nonlinearities. Calculus of Variations and Partial Differential Equations, 46(1-2), 113-122. https://doi.org/10.1007/s00526-011-0476-x (Original work published 2013)