Manuel Zamora: On a periodically forced Liénard differential equation with singular $\phi-$Laplacian, p.327-336

Abstract:

Sufficient conditions are established in order to guarantee the existence of positive periodic solutions to $$\left(\frac{u'}{\sqrt{1-u'^2}}\right)'+f(u)u'=\frac{m(t)}{u^{\mu}}-\frac{n(t)}{u^{\lambda}}+h(t)u^{\delta},$$, where $f:(0,+\infty)\to\RR$, are continuous functions and $\mu,\lambda,\delta\geq 0$.

Key Words: $\phi$-Laplacian, periodic solutions, singular nonlinearity, friction-like term, lower and upper solutions.

2000 Mathematics Subject Classification: Primary: 34B15;
Secondary: 34B16, 34C25.

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