Newton's inequalities for families of complex numbers.
Nonabsolutely convergent series
Assume that for any from an interval a real number is given. Summarizing all these numbers is no problem in case of an absolutely convergent series . The paper gives a rule how to summarize a series of this type which is not absolutely convergent, using a theory of generalized Perron (or Kurzweil) integral.
Non-archimedean monotone functions
Non-Baire unions in category bases.
Non-compact lamination convex hulls
Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum
We construct a Lipschitz function on which is locally convex on the complement of some totally disconnected compact set but not convex. Existence of such function disproves a theorem that appeared in a paper by L. Pasqualini and was also cited by other authors.
Nondifferentiable functions, Haar null sets and Wiener measure
Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group
2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55Denoting by Dα0|t the time-fractional derivative of order α (α ∈ (0, 1)) in the sense of Caputo, and by ∆H the Laplacian operator on the (2N + 1) - dimensional Heisenberg group H^N, we prove some nonexistence results for solutions to problems of the type Dα0|tu − ∆H(au) >= |u|^p, Dα0|tu − ∆H(au) >= |v|^p, Dδ0|tv − ∆H(bv) >= |u|^q, in H^N × R+ , with a, b ∈ L ∞ (H^N × R+). For α = 1 (and δ = 1 in the case of two inequalities),...
Nonlinear contractive conditions: A comparison and related problems
We establish five theorems giving lists of nonlinear contractive conditions which turn out to be mutually equivalent. We derive them from some general lemmas concerning subsets of the plane which may be applied both in the single- or set-valued case as well as for a family of mappings. A separation theorem for concave functions is proved as an auxiliary result. Also, we discuss briefly the following problems for several classes of contractions: stability of procedure of successive approximations,...
Nonlinear delay discrete inequalities and their applications to Volterra type difference equations.
Nonlinear delay integral inequalities for piecewise continuous functions and applications.
Nonlinear delay integrodifferential systems with Caputo fractional derivative in infinite-dimensional spaces
This paper is mainly concerned with existence of mild solutions and optimal controls for nonlinear delay integrodifferential systems with Caputo fractional derivative in infinite-dimensional spaces. We do not assume that the relevant strongly continuous semigroup is compact.
Nonlinear dynamics and chaos in a fractional-order HIV model.
Nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in Banach spaces
We consider a nonlinear fractional differential inclusion with nonlocal fractional integro-differential boundary conditions in a Banach space. The existence of at least one solution is proved by using the set-valued analog of Mönch fixed point theorem associated with the technique of measures of noncompactness.
Nonlinear functional equations and their Baire category properties.
Nonlinear Heat Equation with a Fractional Laplacian in a Disk
For the nonlinear heat equation with a fractional Laplacian , 1 < α ≤ 2, the first initial-boundary value problem in a disk is considered. Small initial conditions, homogeneous boundary conditions, and periodicity conditions in the angular coordinate are imposed. Existence and uniqueness of a global-in-time solution is proved, and the solution is constructed in the form of a series of eigenfunctions of the Laplace operator in the disk. First-order long-time asymptotics of the solution is obtained....
Nonlinear Implicit Hadamard’s Fractional Differential Equationswith Delay in Banach Space
In this paper, we establish sufficient conditions for the existence of solutions for nonlinear Hadamard-type implicit fractional differential equations with finite delay. The proof of the main results is based on the measure of noncompactness and the Darbo’s and Mönch’s fixed point theorems. An example is included to show the applicability of our results.
Nonlinear integral inequalities in two independent variables on time scales.
Nonlinear integral inequalities in two independent variables and their applications.
Nonlinear integral inequality in two independent variables.