Current Issue : July-September Volume : 2023 Issue Number : 3 Articles : 5 Articles
In this article, we establish a nonexistence result of nontrivial non-negative solutions for the following Choquard-type Hamiltonian system by the Pohožaev identity { } { } ( ) ( ) 1 2 2 2 , in \ 0 , , in \ 0 , , 0, when , p p N q q N v v v u u I x x u u u v v I x x u x v x x μ α α μ β β − − −Δ + = ∗ −Δ + = ∗ → →∞ , when N ≥ 3 , 1 2 0 < μ ,μ < N , 0 1 2 μ ≤α ≤ , 0 2 2 μ ≤ β ≤ , p, q > 1 , and 1 2 ( ) 2 2 2 2 N N N p q +μ − α +μ − β + ≤ − , where 1 i N i I x μ −μ = and ∗ denotes the convolution in N , i = 1, 2 ....
In this paper, several results and theorems about the high-order strongly generalized Hukuhara differentiability of function defined via the fuzzy Riemann improper integral (in the sense of Wu) have been established. Then, some properties dealing with the partial derivatives of fuzzy Laplace transform for a fuzzy function of two real variables have been proved. Afterwards, an algorithm of fuzzy Laplace transform for solving second-order fuzzy partial differential equations has been proposed. Finally, two numerical examples, including the heat equation under fuzzy initial conditions, have been studied to justify the efficiency of the algorithm....
This review paper contains computational methods or solution methodologies for singularly perturbed differential difference equations with negative and/or positive shifts in a spatial variable. This survey limits its coverage to singular perturbation equations arising in the modeling of neuronal activity and the methods developed by numerous researchers between 2012 and 2022. The review covered singularly perturbed ordinary delay differential equations with small or large negative shift(s), singularly perturbed ordinary differential–differential equations with mixed shift(s), singularly perturbed delay partial differential equations with small or large negative shift(s) and singularly perturbed partial differential–difference equations of the mixed type. The main aim of this review is to find out what numerical and asymptotic methods were developed in the last ten years to solve such problems. Further, it aims to stimulate researchers to develop new robust methods for solving families of the problems under consideration....
In the fuzzy theory of sets and groups, the use of α-levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong α-levels, it is possible to establish a one to one correspondence which makes possible doubly, a gradual and a functorial treatment of the fuzzy theory. The main result of this paper is to identify the class of fuzzy sets, respectively, fuzzy groups, with subcategories of the functorial categories Set (0, 1], resp., Gr (0, 1]. In this line, the algebraic potential of this theory will be reached, in forthcoming papers....
We extend Bourgain’s bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) t13/84+ as t → ∞. For both, the Riemann zeta function as well as for the more general Lerch zeta function, it is conjectured that the right-hand side can be replaced by t (which is the so-called Lindelöf hypothesis). The growth of an analytic function is closely related to the distribution of its zeros....
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