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Apr 07, 2025Open Access
In this article, our focus lies on a Schrödinger equation incorporating a Hardy term. To identify the global minimizers of the functional I under a mass constraint, we utilize the Hardy inequality. In addition, we reveal that every energy ground state is directly linked to the least action solution of the associated action functional. This finding affirmatively addresses the question of whether, under broad assumptions, The functional &...
Apr 10, 2024Open Access
This paper zeroes in on the existence result of solutions to a fractional Kirchhoff equation with doubly critical exponents, mixed nonlinear terms and a continuous potential V. After utilizing some energy estimates, one obtains the effect of exponents p and q on the existence of constrained minimizers, namely, the connection between the existence of normalized solutions and exponents p, q.
Apr 03, 2024Open Access
In this paper, a semilinear elliptic equation of fractional order is constructed by combining the semilinear elliptic equation with the fractional order equation. On this basis, the “standardized” solution, which is often sought by physicists, is studied. In order to overcome the problem of lack of boundness, we set up appropriate conditions to prove the existence of the solution by means of variational theorem and the mountain road theorem.
Dec 29, 2023Open Access
In this paper, we study the spectral properties of a family of discrete one-dimensional quasi-periodic Schrödinger operators (depending on a phase theta). In the perturbative regime and in large disorder, under some conditions on v and a diophantine rotation number, we prove by using KAM theory that this operator satisfies both Anderson and dynamical localization for all θ∈[0,2π).
Apr 12, 2023Open Access
In this paper, we study the existence of solutions to the fractional Klein-Gordon-Maxwell equations. We use the Lions lemma and the mountain pass theorem to prove the existence of solutions.
Jun 15, 2022Open Access
This paper is concerned with the existence of ground state solutions for p-fractional Choquard-Kirchhoff equations involving electromagnetic fields and critical nonlinearity. Under assumptions on the nonlinear term, by applying the method of Nehari manifold, we obtain that the equation possesses a ground state solution.
Aug 30, 2021Open Access
We investigate the existence of solutions for Klein-Gordon-Maxwell equations involving Hardy-Sobolev critical exponents. By means of the Ekeland’s variational principle and the Mountain Pass Theorem, we obtain that there is at least a nontrivial solution for the subcritical system. Then we prove that there are at least two different solutions for the critical system.
Oct 16, 2020Open Access
Since nonlinear schur theorem was proposed, it broke the limitation of linear operator matrices. And in this paper we study the summability theory for a class of matrices of nonlinear mapping, and the characterizations of a class of infinite matrix transformations are obtained. These results enrich the results on infinite matrices transformations, and have important meaning for the study of Banach space.
Dec 24, 2019Open Access
In this paper, we prove fixed point theorems of a generalization which is related to the concept of Meir-Keeler function in a complete b2-metric space. And we know it extends and generalizes some known results in metric space to b2-metric space.
Aug 29, 2019Open Access
For importance of the trigonometric integrals, we have in this paper finding a series of power, some of trigonometric functions that did not exist before in the first section. As shown in the Section two, where, the integration of trigono-metric function with power n has been achieved and approved, this result is considered as the first achievement. while in the third section we find integrals ...
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