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 \(f\left( u\right)\).


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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