Existence Of Solutions To Two Classes Of Kirchhoff Equations

In the first chapter,we briefly introduce the research background and the main results.In the second chapter,we consider Kirchhoff equation with concave and convex nonlinear terms where the potential V（x）can change its sign,the nonlinear term f（x,u）involves the com-bination of concave and convex terms and b≥0 is a constant.By the variational method,we obtain two different types of non-trivial solutions.In the third chapter,we consider the following Kirchhoff equation with bi-nonlocal terms where ξ>0,a>0,b>0,1<q<2<p<（2_*-2）.2_*:=2N/N-4,if N ≥ 5;2_*:=+∞,if N<4.Because of（?）|u|^pdx and（?）|▽u|²dx,the equation（P₂）is called the bi-nonlocal equation.With the help of critical point theory,we get that（P₂）has mountain-pass solutions,minimal solutions,sign-changing solutions of mountain-pass type,and multiple high energy sign-changing solutions.