Irena Rachunkova, Department of Mathematics, Palacky University, 779 00 Olomouc, Tomkova 40, Czech Republic, e-mail: rachunko@risc.upol.cz; Milan Tvrdy, Mathematical Institute, Academy of Sciences of the Czech Republic, 115 67 Praha 1, Zitna 25, Czech Republic, e-mail: tvrdy@math.cas.cz; Ivo Vrkoc, Mathematical Institute, Academy of Sciences of the Czech Republic, 115 67 Praha 1, Zitna 25, Czech Republic, e-mail: vrkoc@ns.math.cas.cz
Abstract: The paper deals with the boundary value problem
u"+k u=g(u)+e(t),\quad u(0)=u(2\pi), u'(0)=u'(2\pi),
where $k\in\R$, $g \I\mapsto\R$ is continuous, $e\in\LL\J$ and $\lim_{x\to0+}\int_x^1g(s) \dd s=\infty.$ In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.
Keywords: second order nonlinear ordinary differential equation, periodic problem, lower and upper functions
Classification (MSC2000): 34B15, 34C25
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