Search results for "UNIQUE"
showing 10 items of 268 documents
Some Decision Results on Nonrepetitive Words
1985
The paper addresses some generalizations of the Thue Problem such as: given a word u, does there exist an infinite nonrepetitive overlap free (or square free) word having u as a prefix? A solution to this as well as to related problems is given for the case of overlap free words on a binary alphabet.
A new algorithm for the kinetic data analysis
2000
Abstract In this paper, a new algorithm for the kinetic data analysis is presented. The main objective of the algorithm is to retrieve the maximum information concerned with a multi-response complex chemical system evolving in time, in order to retrieve the rate constants (calibration problem) or the initial concentration of species. As a difference with other data treatments found in the literature, the algorithm is able to estimate the uniqueness and reliability of the calculated rate constants. This task is carried out by analyzing of the principal components of the sensitivity coefficients with regard to the rate constants. The analysis allows understanding whether the located stationar…
phi-Best proximity point theorems and applications to variational inequality problems
2017
The main concern of this study is to introduce the notion of $$\varphi $$ -best proximity points and establish the existence and uniqueness of $$\varphi $$ -best proximity point for non-self mappings satisfying $$(F,\varphi )$$ -proximal and $$(F,\varphi )$$ -weak proximal contraction conditions in the context of complete metric spaces. Some examples are supplied to support the usability of our results. As applications of the obtained results, some new best proximity point results in partial metric spaces are presented. Furthermore, sufficient conditions to ensure the existence of a unique solution for a variational inequality problem are also discussed.
Principal eigenvalue of a very badly degenerate operator and applications
2007
Abstract In this paper, we define and investigate the properties of the principal eigenvalue of the singular infinity Laplace operator Δ ∞ u = ( D 2 u D u | D u | ) ⋅ D u | D u | . This operator arises from the optimal Lipschitz extension problem and it plays the same fundamental role in the calculus of variations of L ∞ functionals as the usual Laplacian does in the calculus of variations of L 2 functionals. Our approach to the eigenvalue problem is based on the maximum principle and follows the outline of the celebrated work of Berestycki, Nirenberg and Varadhan [H. Berestycki, L. Nirenberg, S.R.S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operator…
\( L^{1} \) existence and uniqueness results for quasi-linear elliptic equations with nonlinear boundary conditions
2007
Abstract In this paper we study the questions of existence and uniqueness of weak and entropy solutions for equations of type − div a ( x , D u ) + γ ( u ) ∋ ϕ , posed in an open bounded subset Ω of R N , with nonlinear boundary conditions of the form a ( x , D u ) ⋅ η + β ( u ) ∋ ψ . The nonlinear elliptic operator div a ( x , D u ) is modeled on the p-Laplacian operator Δ p ( u ) = div ( | D u | p − 2 D u ) , with p > 1 , γ and β are maximal monotone graphs in R 2 such that 0 ∈ γ ( 0 ) and 0 ∈ β ( 0 ) , and the data ϕ ∈ L 1 ( Ω ) and ψ ∈ L 1 ( ∂ Ω ) .
Fixed point methods and accretivity for perturbed nonlinear equations in Banach spaces
2020
Abstract In this paper we use fixed point theorems to guarantee the existence of solutions for inclusions of the form A u + λ u + F u ∋ g , where A is a quasi-m-accretive operator defined in a Banach space, λ > 0 , and the nonlinear perturbation F satisfies some suitable conditions. We apply the obtained results, among other things, to guarantee the existence of solutions of boundary value problems of the type − Δ ρ ( u ( x ) ) + λ u ( x ) + F u ( x ) = g ( x ) , x ∈ Ω , and ρ ( u ) = 0 on ∂Ω, where the Laplace operator Δ should be understood in the sense of distributions over Ω and to study the existence and uniqueness of solution for a nonlinear integro-differential equation posed in L 1 …
Uniqueness of positive solutions to some nonlinear Neumann problems
2017
Abstract Using the moving plane method, we obtain a Liouville type theorem for nonnegative solutions of the Neumann problem { div ( y a ∇ u ( x , y ) ) = 0 , x ∈ R n , y > 0 , lim y → 0 + y a u y ( x , y ) = − f ( u ( x , 0 ) ) , x ∈ R n , under general nonlinearity assumptions on the function f : R → R for any constant a ∈ ( − 1 , 1 ) .
Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals in the theory of Haar and Walsh series
2015
Abstract The problem of recovering the coefficients of rectangular convergent multiple Haar and Walsh series from their sums, by generalized Fourier formulas, is reduced to the one of recovering a function (the primitive) from its derivative with respect to the appropriate derivation basis. Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals are compared and it is shown that a Perron-type integral, defined by major and minor functions having a special continuity property, solves the coefficients problem for series which are convergent everywhere outside some uniqueness sets.
Stability of the Calderón problem in admissible geometries
2014
In this paper we prove log log type stability estimates for inverse boundary value problems on admissible Riemannian manifolds of dimension n ≥ 3. The stability estimates correspond to the uniqueness results in [13]. These inverse problems arise naturally when studying the anisotropic Calderon problem. peerReviewed
Existence and almost uniqueness for p -harmonic Green functions on bounded domains in metric spaces
2020
We study ($p$-harmonic) singular functions, defined by means of upper gradients, in bounded domains in metric measure spaces. It is shown that singular functions exist if and only if the complement of the domain has positive capacity, and that they satisfy very precise capacitary identities for superlevel sets. Suitably normalized singular functions are called Green functions. Uniqueness of Green functions is largely an open problem beyond unweighted $\mathbf{R}^n$, but we show that all Green functions (in a given domain and with the same singularity) are comparable. As a consequence, for $p$-harmonic functions with a given pole we obtain a similar comparison result near the pole. Various c…