## A global continuation theorem for obtaining eigenvalues and bifurcation points.(English)Zbl 0665.35010

This paper proves the existence of a connected branch of solutions [$$\lambda$$,u,$$\tau$$ ] of the equation $$u- T(\lambda)u+H_{\tau}(\lambda,u)=0$$, $$u\in Banach$$ space with the additional norm condition $$\| u\|^ 2=\delta \tau$$ containing at least one $$[\lambda_{\tau},u_{\tau},\tau]$$ for any $$\tau \in <0,1)$$, starting at $$[\lambda_ 0,0,0]$$ and lying in a suitable subinterval $$J_ 0$$ of J (the interval of $$\lambda)$$. Here $$\lambda\in J$$ is a bifurcation parameter, $$\tau\in (0,1)$$ is an additional parameter, $$\delta >0$$ is fixed.
Reviewer: J.H.Tian

### MSC:

 35B32 Bifurcations in context of PDEs 39B52 Functional equations for functions with more general domains and/or ranges 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35B60 Continuation and prolongation of solutions to PDEs 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 34G20 Nonlinear differential equations in abstract spaces
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### References:

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