Ground states for fractional Kirchhoff double-phase problem with logarithmic nonlinearity

Abstract

Our primary objective is to study the solvability of two kinds of fractional Kirchhoff double-phase problem involving logarithmic nonlinearity in RN{{\mathbb{R}}}^{N} via the variational approach. To address the modulation coefficient in fractional double-phase operators, a new functional framework and the corresponding fractional Musielak-Sobolev space are provided. Among others, the completeness, reflexivity, and uniformly convexity of the space are established, and the continuity, boundedness, and (S+)\left({S}_{+})-property of the fractional double-phase operator are given.

Keywords

• fractional double-phase operator
• fractional musielak-sobolev space
• logarithmic nonlinearity
• mountain pass theorem
• 35r11
• 35d30
• 35j50