Existence and multiplicity of solutions for a Schrodinger-Kirchhoff type equation involving the fractional p(.,.)-Laplacian operator in R-N

Ayazoğlu, Rabil; Saraç, Yeşim; Şener Kılıç, Sıdıka; Alisoy, Gulizar

doi:10.1007/s13348-020-00283-5

Existence and multiplicity of solutions for a Schrodinger-Kirchhoff type equation involving the fractional p(.,.)-Laplacian operator in R-N

Ayazoğlu R., Saraç Y., Şener Kılıç S. Ş., Alisoy G.

COLLECTANEA MATHEMATICA, cilt.72, sa.1, ss.129-156, 2021 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 72 Sayı: 1
Basım Tarihi: 2021
Doi Numarası: 10.1007/s13348-020-00283-5
Dergi Adı: COLLECTANEA MATHEMATICA
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
Sayfa Sayıları: ss.129-156
Anahtar Kelimeler: Fractional Sobolev space with variable exponent, Fractional p(.,.)-Laplacian operator, Schrodinger-Kirchhoff type equations, Mountain pass theorem, Krasnoselskii's genus, ELLIPTIC PROBLEMS, P-LAPLACIAN, P(X)-LAPLACIAN, SPACES
Atatürk Üniversitesi Adresli: Evet

Özet

In this paper, by using variational approach, Mountain Pass Theorem and Krasnoselskii's genus theory, we show the existence and multiplicity of solutions for a Schrodinger-Kirchhoff type equation involving the fractional p-Laplacian in fractional Sobolev space with variable exponent. We also establish a Bartsch-Wang type compact embedding theorem for fractional Sobolev space with variable exponent.