Existence and asymptotical behavior of ground state solutions for fractional Schrödinger-Kirchhoff type equations



	Existence and asymptotical behavior of ground state solutions for fractional Schrödinger-Kirchhoff type equations


	Fixed Point Theory, Volume 25, No. 1, 2024, 399-418, February 1st, 2024 DOI: 10.24193/fpt-ro.2024.1.25 Authors: Chawen Xiong, Chunfang Chen, Jianhua Chen and Jijiang Sun Abstract: In this paper, we study the following Schrödinger-Kirchhoff type equations involving the fractional p-Laplacian M([u]^p_s,p)(-Δ)_p^su+(1+λg(x))u^p-1 = H(x)u^q-1, u > 0, x ∈ ℝ^N, where s ∈ (0, 1), 2 ≤ p < ∞, ps < N and (-Δ)_p^s is the fractional p-Laplacian operator. M(t)=a+bt^k, where a, k > 0 and b ≥ 0 are constants. λ > 0 is a real parameter. p(k+1) < q < p_s^, where p_s^=Np/(N-ps) is the fractional Sobolev critical exponent. Under some appropriate assumptions on g(x) and H(x), we obtain the existence of positive ground state solutions and discuss their asymptotical behavior via the method used by Bartsch and Wang [Multiple positive solutions for a nonlinear Schrödinger equation. Z. Angew. Math. Phys. 51 (2000) 366-384]. Key Words and Phrases: Schrödinger-Kirchhoff equation, fractional p-Laplacian, ground state solution, asymptotical behavior, steep well potential, fixed point. 2010 Mathematics Subject Classification: 35R11, 35J60, 35A15, 35J35, 47H10. Published on-line: February 1st, 2024. Fulltext pdf Back to volume's table of contents