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Multiplicity of solutions for second order two-point boundary value problems with asymptotically asymmetric nonlinearities at resonance. (English) Zbl 1130.34011

The author considers several resonant cases of the two-point boundary value problem \[ \begin{gathered} x''+g(t,x)=f(t,x,x'),\\ x(a)\cos\alpha-x'(a)\sin\alpha=0,\\ x(b)\cos\beta-x'(b)\sin\beta=0,\end{gathered} \] where \(g(t,s)\) is an asymptotically linear nonlinearity, and \(f\) is a sublinear one. Using the angular function technique the author gives estimates of the number of solutions to the above boundary value problem.
Reviewer: Minghe Pei (Jilin)

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
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