Publicationshttp://hdl.handle.net/11141/462019-05-01T13:56:29Z2019-05-01T13:56:29ZSome new nonlinear second-order boundary value problems on an arbitrary domainAlsaedi, AhmedAlsulami, MonaAgarwal, Ravi P.Ahmad, Bashirhttp://hdl.handle.net/11141/27392019-03-08T08:00:55Z2018-12-01T00:00:00ZSome new nonlinear second-order boundary value problems on an arbitrary domain
Alsaedi, Ahmed; Alsulami, Mona; Agarwal, Ravi P.; Ahmad, Bashir
In this paper, we develop the existence theory for nonlinear second-order ordinary differential equations equipped with new kinds of nonlocal non-separated type integral multi-point boundary conditions on an arbitrary domain. Existence results are proved with the aid of fixed point theorems due to Schaefer, Krasnoselskii, and Leray–Schauder, while the uniqueness of solutions for the given problem is established by means of contraction mapping principle. Examples are constructed for the illustration of the obtained results. Ulam-stability is also discussed for the given problem. A variant of the problem involving different boundary data is also discussed. Finally, we introduce an associated boundary value problem involving integro-differential equations and discuss the uniqueness of its solutions.
2018-12-01T00:00:00ZLyapunov Functions to Caputo Fractional Neural Networks with Time-Varying DelaysAgarwal, Ravi P.Hristova, Snezhana G.O'Regan, Donalhttp://hdl.handle.net/11141/25902018-09-20T07:00:43Z2018-05-09T00:00:00ZLyapunov Functions to Caputo Fractional Neural Networks with Time-Varying Delays
Agarwal, Ravi P.; Hristova, Snezhana G.; O'Regan, Donal
One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable). In connection with the Lyapunov fractional method we present a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of neural networks with variable coefficients and time-varying delays. We show that quadratic Lyapunov functions and their Caputo fractional derivatives are not applicable in some cases when one studies stability properties. Some sufficient conditions for stability of equilibrium of nonlinear Caputo fractional neural networks with time dependent transmission delays, time varying self-regulating parameters of all units and time varying functions of the connection between two neurons in the network are obtained. The cases of time varying Lipschitz coefficients as well as nonLipschitz activation functions are studied. We illustrate our theory on particular nonlinear Caputo fractional neural networks.
2018-05-09T00:00:00ZAn existence principle for nonlocal difference boundary value problems with φ-laplacian and its application to singular problemsAgarwal, Ravi P.O'Regan, DonalStaněk, Svatoslavhttp://hdl.handle.net/11141/24462018-05-08T14:13:44Z2008-01-01T00:00:00ZAn existence principle for nonlocal difference boundary value problems with φ-laplacian and its application to singular problems
Agarwal, Ravi P.; O'Regan, Donal; Staněk, Svatoslav
The paper presents an existence principle for solving a large class of nonlocal regular discrete boundary value problems with the ψ-Laplacian. Applications of the existence principle to singular discrete problems are given.
nonlocal regular discrete boundary value problems
2008-01-01T00:00:00ZSuperhyperfine interactions in the electron-spin-resonance spectrum of substitutional gd3+ impurity in caf2 single crystals under applied stressBowden, Charles M.Miller, John E.http://hdl.handle.net/11141/24072018-05-08T13:53:59Z1967-07-03T00:00:00ZSuperhyperfine interactions in the electron-spin-resonance spectrum of substitutional gd3+ impurity in caf2 single crystals under applied stress
Bowden, Charles M.; Miller, John E.
In this communication we report a superhyperfine
structure in the esr spectrum of 0.001
at. ~0 Gd' in a single crystal of CaF, under applied
stress. The stress was applied at the
polished (111)face of the CaF, crystal by a thin
film of Ge applied as an epitaxy. ' Differential
stress was applied to the CaF2 crystal by changing
the temperature of the sample.
1967-07-03T00:00:00Z