We study the existence and multiplicity of solutions for nonlocalperturbed Kirchhoff problem$$\displaylines{-\Big(a+b\int_\Omega |\nabla u|^2\,dx\Big)\Delta u=\lambda g(x,u)+f(x,u), \quad \text{in } \Omega,\\ u=0, \quad\text{on }\partial\Omega,}$$ where Ω is a bounded smooth domain in \(\mathbb{R}^N\), \(N>4\), \(a,b, \lambda > 0\), \(f,g:\Omega\times \mathbb{R}\to \mathbb{R}\) ...

Employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of Neumann two-point boundary valueSturm-Liouville type equations. Using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.