Infinitely Differentiable Functions With Prescribed Derivatives At A Point.
We consider the existence of infinitely many solutions to the boundary value problem Under more general assumptions on the nonlinearity, we obtain new criteria to guarantee that this boundary value problem has infinitely many solutions in the superquadratic, subquadratic and asymptotically quadratic cases by using the critical point theory.
2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analytic solution can be written...
We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some results of Olsen and Snigireva by computing the upper box dimensions assuming some mild separation conditions. Secondly, we investigate the more difficult problem of computing the lower box dimension. We give some non-trivial bounds and provide examples to show that lower box dimension behaves much more strangely than upper box dimension, Hausdorff dimension and packing dimension.
We establish sufficient conditions for the existence of solutions of a class of fractional functional differential inclusions involving the Hadamard fractional derivative with order . Both cases of convex and nonconvex valued right hand side are considered.
We provide a number of either necessary and sufficient or only sufficient conditions on a local homeomorphism defined on an open, connected subset of the n-space to be actually a homeomorphism onto a star-shaped set. The unifying idea is the existence of "auxiliary" scalar functions that enjoy special behaviours along the paths that result from lifting the half-lines that radiate from a point in the codomain space. In our main result this special behaviour is monotonicity, and the auxiliary function...
Necessary and sufficient conditions in terms of lower cut sets are given for the insertion of a Baire- function between two comparable real-valued functions on the topological spaces that -kernel of sets are -sets.
In the shape from shading problem of computer vision one attempts to recover the three-dimensional shape of an object or landscape from the shading on a single image. Under the assumptions that the surface is dusty, distant, and illuminated only from above, the problem reduces to that of solving the eikonal equation |Du|=f on a domain in . Despite various existence and uniqueness theorems for smooth solutions, we show that this problem is unstable, which is catastrophic for general numerical algorithms. ...
In this paper, following the -adic integration theory worked out by A. F. Monna and T. A. Springer [4, 5] and generalized by A. C. M. van Rooij and W. H. Schikhof [6, 7] for the spaces which are not -compacts, we study the class of integrable -adic functions with respect to Bernoulli measures of rank . Among these measures, we characterize those which are invertible and we give their inverse in the form of series.
In this paper we study the existence of integrable solutions for initial value problem for implicit fractional order functional differential equations with infinite delay. Our results are based on Schauder type fixed point theorem and the Banach contraction principle fixed point theorem.
In the setting of spaces of homogeneous-type, we define the Integral, , and Derivative, , operators of order , where is a function of positive lower type and upper type less than , and show that and are bounded from Lipschitz spaces to and respectively, with suitable restrictions on the quasi-increasing function in each case. We also prove that and are bounded from the generalized Besov , with , and Triebel-Lizorkin spaces , with , of order to those of order and respectively,...
Using the generalized Erdélyi-Kober fractional integrals, an attempt is made to establish certain new fractional integral inequalities, related to the weighted version of the Chebyshev functional. The results given earlier by Purohit and Raina (2013) and Dahmani et al. (2011) are special cases of results obtained in present paper.