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Classification and evolution of bifurcation curves for a Dirichlet-Neumann boundary value problem and its application. (English) Zbl 1416.37047

The authors study the following boundary value problem: \[ \begin{gathered} u^{\prime\prime}\left( x\right) +\lambda f\left( u\right) =0,\qquad 0< x <1,\\ u\left( 0\right) =0,\ u^{\prime}\left( 1\right) =-c<0, \end{gathered} \] where \(\lambda>0\) is a bifurcation parameter and \(c>0\) is an evolution parameter. They study the classification and evolution of bifurcation curves of positive solutions for the problem, under some suitable assumptions on the nonlinearity of \(f\left( u\right)\).

MSC:

37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
37G10 Bifurcations of singular points in dynamical systems
34C23 Bifurcation theory for ordinary differential equations
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