On a countable set of normalized eigenfunctions of a nonlinear periodic problem with transformed argument (Q2703891)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a countable set of normalized eigenfunctions of a nonlinear periodic problem with transformed argument |
scientific article |
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26 June 2002
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nonlinear periodic problem
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transformed argument
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normalized eigenfunctions
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On a countable set of normalized eigenfunctions of a nonlinear periodic problem with transformed argument (English)
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The problem NEWLINE\[NEWLINE u''(x)+q(u(\sigma(x)),u'(\sigma(x)),x)u(x)+\lambda u(x)=0, NEWLINE\]NEWLINE NEWLINE\[NEWLINE u(0)=u(\pi),\quad u'(0)=u'(\pi),\qquad \int_0^{\pi}u^2(x) dx=R^2,\quad R>0 NEWLINE\]NEWLINE is considered. A Lyusternik-type theorem is proved. The main result provides conditions under which the problem has at least two solutions (one of them is positive, the other is negative) with zero index, countably many normalized solutions (among which there are solutions with arbitrary large indices), and double solutions with given index. Consequences concerning bifurcation points are given.
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