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Persistence and bifurcation of degenerate solutions. (English) Zbl 0949.47050

The author studies an equation \(F(\varepsilon,\lambda,u)=0\), where \(F:{\mathbb R}\times {\mathbb R}\times X\rightarrow Y\) is a smooth nonlinear map and \(X, Y\) are Banach spaces. It is obtained a number of bifurcation results for degenerate solutions. Several applications to elliptic boundary value problems of the form \(Lu+\lambda f(\varepsilon, u)=0\) are presented.

MSC:

47J15 Abstract bifurcation theory involving nonlinear operators
35B32 Bifurcations in context of PDEs
35J60 Nonlinear elliptic equations
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