## 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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### References:

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