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A bifurcation theorem for noncoercive integral functionals. (English) Zbl 1098.35019

Existence of critical points for noncoercive functionals of the form \[ J_\lambda (v)={1 \over 2}\int _\Omega a(x,v)| \nabla v| ^2-\lambda \int _\Omega F(x,v) \] whose principal part has a degenerate coerciveness is studied. The author proves an existence of critical points of \(J_\lambda \) for small \(\lambda \), assuming a suitable behaviour of the nonlinearity \(F\) at zero. A bifurcation result at \(\lambda =0\) for \(J'_\lambda \) in \(H^1_0\) is established. Examples demonstrating the improvement of known results are given.

MSC:

35B32 Bifurcations in context of PDEs
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals)
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