Geodesic
Upper and Lower Solutions Method for Darboux Problem for Fractional Order Implicit Impulsive Partial Hyperbolic Differential Equations
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 51 (2012) no. 2, pp. 5-18 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we investigate the existence of solutions for the initial value problems (IVP for short), for a class of implicit impulsive hyperbolic differential equations by using the lower and upper solutions method combined with Schauder’s fixed point theorem.
In this paper we investigate the existence of solutions for the initial value problems (IVP for short), for a class of implicit impulsive hyperbolic differential equations by using the lower and upper solutions method combined with Schauder’s fixed point theorem.
Classification : 26A33, 35A01, 35R11, 35R12
Keywords: partial hyperbolic differential equation; fractional order; left-sided mixed; Riemann–Liouville integral; mixed regularized derivative; impulse; upper solution; lower solution; fixed point 
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     author = {Abbas, Sa{\"\i}d and Benchohra, Mouffak},
     title = {Upper and {Lower} {Solutions} {Method} for {Darboux} {Problem} for {Fractional} {Order} {Implicit} {Impulsive} {Partial} {Hyperbolic} {Differential} {Equations}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {5--18},
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Abbas, Saïd; Benchohra, Mouffak. Upper and Lower Solutions Method for Darboux Problem for Fractional Order Implicit Impulsive Partial Hyperbolic Differential Equations. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 51 (2012) no. 2, pp. 5-18. http://geodesic.mathdoc.fr/item/AUPO_2012_51_2_a0/