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1
Content available Some new existence results and stability concepts for fractional partial random differential equations
Abbas S., Benchohra M., Darwish M. A.
Journal of Mathematics and Applications
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2016
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Vol. 39
5--22
EN
In the present paper we provide some existence results and Ulam’s type stability concepts for the Darboux problem of partial fractional random differential equations in Banach spaces, by applying the measure of noncompactness and a random fixed point theorem with stochastic domain.
2
Global existence and stability results for partial fractional random differential equations
Abbas S., Albarakati W., Benchohra M., Hilal E.
Journal of Applied Analysis
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2015
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Vol. 21, nr 2
79--87
EN
We investigate some existence and stability results for the Darboux problem of partial fractional random differential equations in Banach spaces. Our existence results are based upon some fixed point theorems.
3
Content available Global convergence of successive approximations of the Darboux problem for partial functional differential equations with infinite delay
Człapiński T.
Opuscula Mathematica
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2014
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Vol. 34, no. 2
327--338
EN
We consider the Darboux problem for the hyperbolic partial functional differential equation with infinite delay. We deal with generalized (in the "almost everywhere" sense) solutions of this problem. We prove a theorem on the global convergence of successive approximations to a unique solution of the Darboux problem.
4
Content available remote Ulam stabilities for the Darboux problem for partial fractional differential inclusions
Abbas S., Benchohra M.
Demonstratio Mathematica
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2014
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Vol. 47, nr 4
826--838
EN
In this article, we investigate some Ulam’s type stability concepts for the Darboux problem of partial fractional differential inclusions with a nonconvex valued right hand side. Our results are based upon Covitz-Nadler fixed point theorem and fractional version of Gronwall’s inequality.
5
Content available remote Application of measures of weak noncompactness to a nonlocal Darboux problem
Majcher P., Sharma S.
Demonstratio Mathematica
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2009
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Vol. 42, nr 3
521-531
EN
In this paper we study the existence of pseudosolutions of a nonlocal hyperbolic Darboux problem for the equation [...] with nonlocal boundary conditions u(x,0) + h1(x,u) = g1(x),u(0,y) + h2(y,u)=g2(y), on the bounded region. The functions considered have values in a Banach space and are weakly-weakly sequentially continuous, and the relevant integrals are Pettis integrals.
6
Content available remote The nonlocal Darboux problem on the unbounded region in Banach spaces
Majcher P.
Demonstratio Mathematica
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2008
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Vol. 41, nr 2
389-402
EN
In this paper we study existence theorems of solutions for the hyperbolic Darboux problem of the form [..] with nonlocal boundary conditions u(x, 0) +h1(u) = g1(x),u(0,y) +h2(u)= g2(y), on the unbounded region. The functions defining nonlocal conditions satisfy the Lipschitz condition with respect to a measure of noncompactness.
7
Content available remote The method of quasilinearization for system of hyperbolic functional differential equations
Karpowicz A.
Commentationes Mathematicae
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2008
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Vol. 48, [Z] 2
155-168
EN
We deal with monotone iterative method for the Darboux problem for the system of hyperbolic partial functional-differential equations. [zob. pełny tekst: http://www.staff.amu.edu.pl/~commath/papers/482/4825.pdf]
8
Content available remote On extremal solutions of differential equations with advanced argument
Augustynowicz A., Jankowski J.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2006
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Vol. 46, [Z] 1
17-24
EN
We obtain existence of absolutely continuous extremal solutions of the problem u'(x) = F(x, u(x), u(h(x))), u(0) = u0, and the Darboux problem for u_xy(x, y) = G(x, y, u(x, y), u(H(x, y))), where h and H are arbitrary continuous deviated arguments.
9
Content available remote Existence and uniqueness of classical solutions to semilinear Darboux problems together with nonstandard conditions with integrals
Byszewski L.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2003
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[Z] 43(2)
169-183
EN
The existence and uniqueness of classical solutions to semilinear hyperbolic differential Darboux problems for the equation [formula] together with nonstandard conditions with integrals in bounded and unbounded domains are studied.
10
Content available remote On the existence of weak solutions of the Darboux problem for the hyperbolic partial differential equations in Banach spaces
Kubiaczyk I., Mostafa Ali N.
Fasciculi Mathematici
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1998
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Nr 28
93-99
EN
In this paper we prove an existence theorem for the hyperbolic partial differential equation zx.y = f(x,y,z,zxy), z(x,O)=o, z(O,y)=O for x,y>O, where Zxy means the second mixed derivative in the weak sence. The continuity of the xy function f is replaced by the weak continuity and the compactness condition is expressed in ternls of the measuresa of weak noncompactness. This paper extends some previous results for our equation.
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