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101.
Hernán R. Henríquez Verónica Poblete Juan C. Pozo 《Journal of Mathematical Analysis and Applications》2014
In this paper we establish the existence of mild solutions for a non-autonomous abstract semi-linear second order differential equation submitted to nonlocal initial conditions. Our approach relies on the existence of an evolution operator for the corresponding linear equation and the properties of the Hausdorff measure of non-compactness. 相似文献
102.
By exploiting a suitable Trudinger–Moser inequality for fractional Sobolev spaces, we obtain existence and multiplicity of solutions for a class of one-dimensional nonlocal equations with fractional diffusion and nonlinearity at exponential growth. 相似文献
103.
104.
Considerable work has gone into studying the properties of nonlocal diffusion equations. The existence of a principal eigenvalue has been a significant portion of this work. While there are good results for the existence of a principal eigenvalue equations on a bounded domain, few results exist for unbounded domains. On bounded domains, the Krein–Rutman theorem on Banach spaces is a common tool for showing existence. This article shows that generalized Krein–Rutman can be used on unbounded domains and that the theory of positive operators can serve as a powerful tool in the analysis of nonlocal diffusion equations. In particular, a useful sufficient condition for the existence of a principal eigenvalue is given. 相似文献
105.
In this paper, we consider a class of nonlocal stochastic Kuramoto–Sivashinsky equations driven by additive noises. Under some appropriate conditions, we investigate long time behavior, i.e., stability and growth bounds of the solutions to the equation. Finally, several examples are given to illustrate our results. 相似文献
106.
Nicola Abatangelo 《Numerical Functional Analysis & Optimization》2014,35(7-9):793-815
We consider a nonlocal (or fractional) curvature and we investigate similarities and differences with respect to the classical local case. In particular, we show that the nonlocal mean curvature can be seen as an average of suitable nonlocal directional curvatures and there is a natural asymptotic convergence to the classical case. Nevertheless, different from the classical cases, minimal and maximal nonlocal directional curvatures are not in general attained at perpendicular directions and, in fact, one can arbitrarily prescribe the set of extremal directions for nonlocal directional curvatures. Also the classical directional curvatures naturally enjoy some linear properties that are lost in the nonlocal framework. In this sense, nonlocal directional curvatures are somewhat intrinsically nonlinear. 相似文献
108.
109.
In this paper, we prove a Hadamard property and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with a gradient term, both in the whole space and in an exterior domain. 相似文献
110.
Ernesto Sánchez‐Mendoza Jesús Hernández‐Trujillo 《Magnetic resonance in chemistry : MRC》2010,48(11):866-872
The indirect vicinal proton–proton coupling constants for pyrrole, furan, thiophene and 15 related heteroaromatic compounds were calculated using the Khon–Sham approximation. An analysis of the four Ramsey contributions to the coupling constants was carried out showing that the Fermi contact term is always positive and dominant, although the remaining contributions have a nonnegligible net negative contribution. The trends observed for the proton–proton coupling constants were rationalized in terms of the properties of the electron density. It was found that electron delocalization between the corresponding hydrogen atoms plays a major role on the observed behavior with the charges of the carbon atoms bonded to them and the accompanying geometric variations being also of importance in the coupling mechanism. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献