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A multiplicity result for quasilinear problems with convex andconcave nonlinearities and nonlinear boundary conditions in unbounded domains

Kandylakis Dimitrios

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URIhttp://purl.tuc.gr/dl/dias/509DC46F-5781-4063-8C94-E02B73A72C77-
Αναγνωριστικόftp://ftp2.de.freebsd.org/pub/EMIS/journals/EJDE/2005/57/kandilakis.pdf-
Γλώσσαen-
Μέγεθος11en
ΤίτλοςA multiplicity result for quasilinear problems with convex and concave nonlinearities and nonlinear boundary conditions in unbounded domainsen
ΔημιουργόςKandylakis Dimitriosen
ΔημιουργόςΚανδυλακης Δημητριοςel
ΠεριγραφήΔημοσίευση σε επιστημονικό περιοδικό el
ΠερίληψηWe study the following quasilinear problem with nonlinear boundary conditions −∆pu = λa(x)|u| p−2u + k(x)|u| q−2u − h(x)|u| s−2u, in Ω, |∇u| p−2∇u · η + b(x)|u| p−2u = 0 on ∂Ω, where Ω is an unbounded domain in RN with a noncompact and smooth boundary ∂Ω, η denotes the unit outward normal vector on ∂Ω, ∆pu = div(|∇u| p−2∇u) is the p-Laplacian, a, k, h and b are nonnegative essentially bounded functions, q < p < s and p ∗ < s. The properties of the first eigenvalue λ1 and the associated eigenvectors of the related eigenvalue problem are examined. Then it is shown that if λ < λ1, the original problem admits an infi- nite number of solutions one of which is nonnegative, while if λ = λ1 it admits at least one nonnegative solution. Our approach is variational in characterel
ΤύποςPeer-Reviewed Journal Publicationen
ΤύποςΔημοσίευση σε Περιοδικό με Κριτέςel
Άδεια Χρήσηςhttp://creativecommons.org/licenses/by/4.0/en
Ημερομηνία2015-10-29-
Ημερομηνία Δημοσίευσης2005-
Βιβλιογραφική ΑναφοράD.A. Kandilakis, "A multiplicity result for quasilinear problems with convex and concave nonlinearities and nonlinear boundary conditions in unbounded domain,"Electronic Journal of Differential Equations, vol. 2005, no. 57, pp. 1–12, 2005.en

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