Bifurcation from infinity and multiple solutions for periodic boundary value problems (Q1576549)

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 \textit{J. Mawhin} and \textit{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.