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Numerical global bifurcation diagrams for a superlinear indefinite problem with a parameter appearing in the domain. (English) Zbl 1460.65157

Summary: We consider a superlinear indefinite problem with homogeneous Neumann boundary conditions and a parameter appearing in the domain of the differential equation. Such a problem is an extension of the one studied by the author [J. Math. Anal. Appl. 467, No. 1, 673–698 (2018; Zbl 1421.34020)], in the sense that also negative values of the parameter are allowed.
First, we show how to discretize the problem in a way that is suitable to perform numerical continuation methods and obtain the associated bifurcation diagrams. Then, we analyze the results of the simulations, also studying the stability of the solutions.

MSC:

65P30 Numerical bifurcation problems
37M20 Computational methods for bifurcation problems in dynamical systems

Citations:

Zbl 1421.34020
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References:

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