Geodesic
Periodic BVP with $\phi$-Laplacian and impulses
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 44 (2005) no. 1, pp. 131-150.

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The paper deals with the impulsive boundary value problem \[ \frac{d}{dt}[\phi (y^{\prime }(t))] = f(t, y(t), y^{\prime }(t)), \quad y(0) = y(T),\quad y^{\prime }(0) = y^{\prime }(T), y(t_{i}+) = J_{i}(y(t_{i})), \quad y^{\prime }(t_{i}+) = M_{i}(y^{\prime }(t_{i})),\quad i = 1, \ldots m. \] The method of lower and upper solutions is directly applied to obtain the results for this problems whose right-hand sides either fulfil conditions of the sign type or satisfy one-sided growth conditions.
Classification : 34B37, 34C25
Keywords: $\phi $-Laplacian; impulses; lower and upper functions; periodic boundary value problem 
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     author = {Pol\'a\v{s}ek, Vladim{\'\i}r},
     title = {Periodic {BVP} with $\phi${-Laplacian} and impulses},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
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Polášek, Vladimír. Periodic BVP with $\phi$-Laplacian and impulses. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 44 (2005) no. 1, pp. 131-150. http://geodesic.mathdoc.fr/item/AUPO_2005__44_1_a11/