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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.

MSC:

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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