Infinitely many sign-changing solutions for Kirchhoff type problems in R[sup]3Sun, Jijiang (Avtor) Li, Lin (Avtor) Cencelj, Matija (Avtor) Gabrovšek, Boštjan (Avtor) infinitely many sign-changing solutionsKirchhoff type problemsinvariant setsdescending flowIn this paper, we consider the following nonlinear Kirchhoff type problem: ▫$$\begin{cases} - \Big (a+b \int_{\mathbb{R}^3} |\nabla u|^2 \Big) \Delta u + V(x)u = f(u), & \text{in} \quad \mathbb{R}^3 \; , \\ u \in H^1 (\mathbb{R}^3) \; , \end{cases}$$▫ where ▫$a,b > 0$▫ are constants, the nonlinearity ▫$f$▫ is superlinear at infinity with subcritical growth and ▫$V$▫ is continuous and coercive. For the case when ▫$f$▫ is odd in ▫$u$▫ we obtain infinitely many sign-changing solutions for the above problem by using a combination of invariant sets method and the Ljusternik-Schnirelman type minimax method. To the best of our knowledge, there are only few existence results for this problem. It is worth mentioning that the nonlinear term may not be 4-superlinear at infinity, in particular, it includes the power-type nonlinearity ▫$|u|^{p-2}u$▫ with ▫$p \in (2, 4]$▫.20192020-05-06 11:33:22Članek v reviji115999UDK: 517.956ISSN pri članku: 0362-546XDOI: 10.1016/j.na.2018.10.007COBISS_ID: 18506585OceCobissID: 26027520sl