POSITIVE HIGH ENERGY SOLUTION FOR KIRCHHOFF EQUATION IN R3 WITH SUPERLINEAR NONLINEARITIES VIA NEHARI-POHOZAEV MANIFOLD

In this paper, we study the following nonlinear problem of Kirch-ho ff type: { -(a + b integral(R3) vertical bar del u vertical bar(2) ) Delta u + V (x)u = f (u), x is an element of R-3 u > 0 x is an element of R-3 where a; b > 0 are constants, V : R-3 -> R and f ( t) is subcritical and superlinear at infinity. Under certain assumptions on non-constant potential V, we prove the existence of positive high energy solutions by using a linking argument with a barycenter map restricted on a Nehari-Pohozaev type manifold. Our main result has solved Kirchhoff equation ( 0.1) with superlinear nonlinearities, which has not been studied, and can be viewed as a partial extension of a recent result of He and Zou in [9] concerning Kirchho ff equations with 4-superlinear nonlinearities.