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Bifurcation from infinity and multiple solutions for periodic boundary value problems. (English) Zbl 0966.34015
The author deals with the existence of multiple solutions to the problem $$u''+\lambda u+ g(u)= h(t),\quad u(0)- u(2\pi)= u'(0)- u'(2\pi)= 0,$$ when the parameter $\lambda$ runs near $m^2$, the $(m+1)$th eigenvalue of the operator $Lu=-u''$ under the periodic conditions. The proofs are based on the topological degree and bifurcation theory. The results complement those obtained by {\it J. Mawhin} and {\it K. Schmitt} [Result. Math. 14, No. 1/2, 138-146 (1988; Zbl 0780.35043)] for the case when $\lambda$ is near $\lambda_1= 0$, and in [Ann. Polon. Math. 51, 241-248 (1990; Zbl 0724.34025)] for some similar twopoint boundary value problems, when a simple eigenvalue is acrossed.

34B15Nonlinear boundary value problems for ODE
34C23Bifurcation (ODE)
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