High energy solutions of general Kirchhoff type equations without the Ambrosetti-Rabinowitz type condition

Abstract In this article, we study the following general Kirchhoff type equation: ? M ? R 3 ? ? u 2 mathvariant="normal">d x mathvariant="normal">? + = a ( ) f mathvariant="normal">in width="0.33em" , -M\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}| \nabla u{| }^{2}{\rm{d}}x\right)\Delta u+u=a\left(x)f\left(u)\hspace{1em}{\rm{in}}\hspace{0.33em}{{\mathbb{R}}}^{3}, where xmlns:m="http://www.w3.org/1998/Math/MathML"> inf > 0 {\inf }_{{{\mathbb{R}}}^{+}}M\gt 0 and f is a superlinear subcritical term. By using Pohoz?ev manifold, obtain existence of high energy solutions aforementioned equation without well-known Ambrosetti-Rabinowitz condition.