EXISTENCE AND ASYMPTOTICAL BEHAVIOR OF GROUND STATE SOLUTIONS FOR FRACTIONAL SCHRODINGER-KIRCHHOFF TYPE EQUATIONS

In this paper, we study the following Schrodinger-Kirchhoff type equations involving the fractional p -Laplacian M([u](s,p)(p))(-Delta)(p)(s)u + (1 + lambda g(x))u(p-1) = H(x)u(q-1), u > 0, x is an element of R-N, where s is an element of (0, 1), 2 <= p < infinity, ps < N and (-Delta)(p)(s) is the fractional p -Laplacian operator. M(t) = a + bt(k), where a, k > 0 and b >= 0 are constants. lambda > 0 is a real parameter. p(k + 1) < q < p(s)(& lowast;), where p(s)(& lowast;)= 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 Schrodinger equation. Z. Angew. Math. Phys. 51 (2000) 366-384].