Abstract A Kirchhoff-type problem with concave-convex nonlinearities is studied. By constrained variational methods on a Nehari manifold, we prove that this has sign-changing solution least energy. Moreover, show the energy level of strictly larger than double ground state solution.

In this paper, we study the initial boundary value problem of important hyperbolic Kirchhoff equation $$\begin{aligned} u_{tt}-\left( a \int _\text{\O}mega |\nabla u|^2 \mathrm {d}x +b\right) \Delta u = \lambda u+ |u|^{p-1}u , \end{aligned}$$ where a, $$b>0$$ $$p>1$$ $$\lambda \in {\mathbb {R}}$$ and energy is arbitrarily large. We prove several new theorems on dynamics such as boundedness or f...

Abstract We study the one-dimensional Kirchhoff-type equation − ( b + a ‖ u accent="false">′ 2 ) accent="true">″ x = <...

In this article, we study a Kirchhoff type problem with nonlinear Neumann boundary conditions on a bounded domain. By using variational methods, we prove the existence of infinitely many solutions.