Ground state solutions of Pohozaev type for Kirchhoff-type problems with general convolution nonlinearity and variable potential

摘要

This paper is devoted to dealing with the following nonlinear Kirchhoff-type problem with general convolution nonlinearity and variable potential: @@@ {-(a + b integral(R3) |del u|(2) dx)Delta u + V(x)u = (I-alpha * F(u)) integral(u), in R-3, @@@ u is an element of H-1(R-3), @@@ where a > 0, b >= 0 are constants; V is an element of C-1(R-3, [0, +infinity)); integral is an element of C(R, R), F(t) = integral(t)(0) integral(s)ds; and I-alpha : R-3 -> R is the Riesz potential, alpha is an element of(0, 3). By applying some new analytical tricks introduced by Tang and Chen, the existence results of ground state solutions of Pohozaev type for the above Kirchhoff type problem are obtained under some mild assumptions on V and the general "Berestycki-Lions assumptions" on the nonlinearity integral. Our results generalize and improve the ones obtained by Chen and Liu and other related results in the literature.

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