Geodesic
Periodic solutions of dissipative dynamical systems with singular potential and $p$-Laplacian
Bing Liu1
1Department of Mathematics Huazhong University of Science and Technology Wuhan 430074, P.R. China and College of Mathematics and Statistics Wuhan University Wuhan 430072, P.R. China
Annales Polonici Mathematici, Tome 79 (2002) no. 2, pp. 109-120
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By using the topological degree theory and some analytic methods, we consider the periodic boundary value problem for the singular dissipative dynamical systems with $p$-Laplacian: $(\phi _p(x'))'+{d\over dt}\mathop {\rm grad}\nolimits F(x)+\mathop {\rm grad}\nolimits G(x)=e(t)$, $x(0)=x(T)$, $x'(0)=x'(T)$. Sufficient conditions to guarantee the existence of solutions are obtained under no restriction on the damping forces ${d\over dt}\mathop {\rm grad}\nolimits F(x)$.
DOI : 10.4064/ap79-2-2
Keywords: using topological degree theory analytic methods consider periodic boundary value problem singular dissipative dynamical systems p laplacian phi mathop grad nolimits mathop grad nolimits sufficient conditions guarantee existence solutions obtained under restriction damping forces mathop grad nolimits

Bing Liu  1

1 Department of Mathematics Huazhong University of Science and Technology Wuhan 430074, P.R. China and College of Mathematics and Statistics Wuhan University Wuhan 430072, P.R. China 
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Bing Liu. Periodic solutions of dissipative dynamical systems
with singular potential and $p$-Laplacian. Annales Polonici Mathematici, Tome 79 (2002) no. 2, pp. 109-120. doi: 10.4064/ap79-2-2

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