# Second Order Periodic with $\phi$-Laplacian and Impulses - Part II

## Irena Rachunkova and Milan Tvrdy

Irena Rachunkova, Department of Math., Palacky University, 779 00 OLOMOUC, Tomkova 40, Czech Republic, e-mail: rachunko@risc.upol.cz;
Milan Tvrdy, Mathematical Institute, Acad. Sci.of the Czech Republic, 115 67 PRAHA 1, Zitna 25, Czech Republic, e-mail: tvrdy@math.cas.cz, http://www.math.cas.cz/~tvrdy/;

Summary:

Existence principles for the~BVP $(\phi(u'))'=f(t,u,u'),$ $u(t_i+)= J_i(u(t_i)),$ $u'(t_i+)= M_i(u'(t_i)),$ $i=1,2,\dots, m,$ $u(0)=u(T),$ $u'(0)=u'(T)$ are presented. They are based on the method of lower/upper functions which are not well-ordered. We continue our investigations from our previous preprint (155/2004), where existence principles based on well-ordered lower/upper functions were proved and from our previous papers, where we delivered related results for the case that $\phi$ is the identity.

Keywords:   $\phi$-Laplacian, impulses, lower/upper functions, periodic solutions, topological degree.

Mathematics Subject Classification: 2000: 34B37, 34B15, 34C25.