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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 $\bbfR^N$, $a,b>0$ 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.

35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35J65Nonlinear boundary value problems for linear elliptic equations
45K05Integro-partial differential equations
Full Text: DOI
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