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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.

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