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Sign-changing solutions of a class of nonlocal quasilinear elliptic boundary value problems. (English) Zbl 1222.35092

Summary: This paper is concerned with nonlocal Kirchhoff’s equation
\[ \begin{cases} -\left(a+b\int_\Omega |\nabla u|^2\right)\Delta u=f(x,u) &\text{in }\Omega,\\ u=0 &\text{on }\partial\Omega, \end{cases} \]
via variational methods and invariant sets of descent flow. We obtain existence of signed and sign-changing solutions with asymptotically 3-linear bounded nonlinearity.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35J62 Quasilinear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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