Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow. (English) Zbl 1100.35008

In the present study the authors obtain sing-changing solutions of the problem: \[ -\left(a+b\int_\Omega|\nabla u|^2\,dx\right)\Delta u=f (x,u),\quad \text{in }\Omega, \qquad u=0,\quad\text{on }\partial\Omega,\tag{1} \] where \(\Omega\) is a smooth bounded domain in \(\mathbb{R}^N\), \(a,b>0\) and \(f\) is a given function. Under suitable assumptions on the data, the authors obtain sign-changing solutions for (1). To this end, they use variational methods and invariant sets of descent flow.


35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
45K05 Integro-partial differential equations
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