Variational methods for nonlinear perturbations of singular φ-Laplacians
(2011) Accademia Nazionale dei Lincei. Atti. Matematica e Applicazioni. Rendiconti — Vol. 22, n° 1, p. 89-111 (2011)
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- Motivated by the existence of radial solutions to the Neumann problem involving the mean extrinsic curvature operator in Minkowski space div(EQUATION PRESANT) where 0 ≤ R<inf>1</inf> < R<inf>2</inf>, A = {x a R<sup>N</sup>: R<inf>1</inf> ≤ |x| a R<inf>2</inf>} and g: [R<inf>1</inf>; R<inf>2</inf>]x R → R is continuous, we study the more general problem [r<sup>N</sup>- <sup>1</sup>φ{u')]' = r<sup>N</sup>-<sup>1</sup>g(r;u); u'(R<inf>1</inf>) = 0 = u'{R<inf>2</inf>); where φ:= φ′: (-a;a) → R is an increasing homeomorphism with φ(0) = 0 and the continuous function φ: [-a; a] → R is of class C<sup>1</sup> on (-a; a). The associated functional in the space of continuous functions over [R1; R<inf>2</inf>] is the sum of a convex lower semicontinuous functional and of a functional of class C <sup>1</sup>. Using the critical point theory of Szulkin, we obtain various existence and multiplicity results for several classes of nonlinearities. We also discuss the case of the periodic problem.
Citations
Bereanu, C., Jebelean, P., & Mawhin, J. (2011). Variational methods for nonlinear perturbations of singular φ-Laplacians. Accademia Nazionale dei Lincei. Atti. Matematica e Applicazioni. Rendiconti, 22(1), 89-111. https://doi.org/10.4171/RLM/589 (Original work published 2011)