Perturbation of periodic boundary conditions. II: Bifurcation and symmetry (Q1105107)
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scientific article; zbMATH DE number 4057992
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Perturbation of periodic boundary conditions. II: Bifurcation and symmetry |
scientific article; zbMATH DE number 4057992 |
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Perturbation of periodic boundary conditions. II: Bifurcation and symmetry (English)
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1987
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[For part I see SIAM J. Math. Anal. 15, 648-655 (1984; Zbl 0545.34014.] The author continues his study of perturbations of the problem \(- x''+bx=\lambda ax,\) \(x(0)-x(1)=0\) both by changes of boundary conditions and by addition of nonlinear terms. He assumes that for \(\lambda =\lambda_ 0\) there are two linearly independent solutions to this problem and the method of Lyapunov and Schmidt is used to analyse the full nonlinear problem. It is shown that when the perturbed problem retains some of the symmetry and is not too degenerate one can use results of Shearer and basic group-theoretical techniques.
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second order differential equation
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perturbations
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0.9185524
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