MULTIPLICITY RESULTS OF CRITICAL LOCAL EQUATION RELATED TO THE GENUS THEORY

Alimohammady M., Rezvani A., Tunç C.

Communications of the Korean Mathematical Society, cilt.38, sa.4, ss.1045-1061, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 4
  • Basım Tarihi: 2023
  • Doi Numarası: 10.4134/ckms.c220308
  • Dergi Adı: Communications of the Korean Mathematical Society
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Sayfa Sayıları: ss.1045-1061
  • Anahtar Kelimeler: genus theory, modular function, p(x)-Laplacian
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Using variational methods, Krasnoselskii’s genus theory and symmetric mountain pass theorem, we introduce the existence and multiplicity of solutions of a parameteric local equation. At first, we consider the following equation (Formula presented) where Ω (Formula presented) (Formula presented) is a bounded domain, µ, is a positive real parameter, p, r and s are continuous real functions on (Formula presented) and a(x,(Formula presented)) is of type |(Formula presented)|p(x)—2. Next, we study boundedness and simplicity of eigenfunction for the case a(x, |(Formula presented)u|)(Formula presented)u = g(x)|(Formula presented)u|p(x)-2(Formula presented)u, where g (Formula presented) L∞(Q) and g(x) > 0 and the case a(x, |(Formula presented)u|)(Formula presented)u = (1 + (Formula presented)u|2)(Formula presented) (Formula presented)u such that p(x) = p.