Open AccessVariational methods for nonlinear perturbations of singular <i>ϕ</i>-Laplacians
Author(s) -
Cristian Bereanu,
Petru Jebelean,
Jean Mawhin
Publication year - 2011
Publication title -
atti della accademia nazionale dei lincei. rendiconti lincei. matematica e applicazioni
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.824
H-Index - 28
eISSN - 1720-0768
pISSN - 1120-6330
DOI - 10.4171/rlm/589
Subject(s) - nabla symbol , combinatorics , multiplicity (mathematics) , homeomorphism (graph theory) , physics , minkowski space , space (punctuation) , mathematics , mathematical physics , mathematical analysis , quantum mechanics , linguistics , philosophy , omega
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 ≤ R1 < R2 , A = {x a RN: R1 ≤ |x| a R2 } and g: [R1 ; R2 ]x R → R is continuous, we study the more general problem [rN- 1φ{u')]' = rN-1g(r;u); u'(R1 ) = 0 = u'{R2 ); 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 C1 on (-a; a). The associated functional in the space of continuous functions over [R1; R2 ] is the sum of a convex lower semicontinuous functional and of a functional of class C 1. 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