Existence of multiple solutions of Schrodinger-Kirchhoff-type equations involving the p(.) -Laplacian in RN
Küçük Resim Yok
Tarih
2020
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Wiley
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this paper, we prove the existence of multiple solutions for the nonhomogeneous Schrodinger-Kirchhoff-type problem involving the p(.)-Laplacian {-(1+b integral(N)(R)1/p(x)vertical bar del u vertical bar(p(x)) dx) Delta(p(x))u+V(x)vertical bar u vertical bar p((x)-2) u=f(x,u) + g(x) in R-N, u is an element of W-1,W-p(.)(R-N), where b >= 0 is a constant, N >= 2, Delta(p)(.)u := div(vertical bar del u vertical bar p((.)-2)del u) is the p(.)-Laplacian operator, p : R-N -> R is Lipschitz continuous, V : R-N -> R is a coercive type potential, integral : R-N x R -> R and g : R-N -> R functions verifying suitable conditions. We propose different assumptions on the nonlinear term f : R-N x R -> R to yield bounded Palais-Smale sequences and then prove that the special sequences we found converge to critical points, respectively. The solutions are obtained by the Mountain Pass Theorem, Ekeland variational principle, and Krasnoselskii genus theory.
Açıklama
Anahtar Kelimeler
Ekeland variational principle, Krasnoselskii genus theory, Lebesgue and Sobolev space with variable exponent, Mountain Pass Theorem, p(.)-Laplacian, Schrodinger-Kirchhoff-type equation
Kaynak
Mathematical Methods in the Applied Sciences
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
43
Sayı
17
