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Periodic solutions of nonlinear perturbations of $$\phi$$-Laplacians with possibly bounded $$\phi$$. (English) Zbl 1147.34032
Using Leray-Schauder degree theory various existence and multiplicity results for nonlinear periodic boundary-value problems of the form $(\phi(u'))'=f(t,u,u'), \qquad u(0)-u(T)=0=u'(0)-u'(T),$ where $$\phi:\mathbb R\to]-a,a[\;(0<a\leq+\infty)$$ is a homeomorphism, $$\phi=0$$ and $$f:[0,T]\times\mathbb R^2\to\mathbb R$$ is a continuous function.

MSC:
 34C25 Periodic solutions to ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34B16 Singular nonlinear boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations
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References:
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