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In this paper, we establish the existence and uniqueness of a time‐periodic solution to the full compressible quantum Euler equations. First, we prove the existence of time‐periodic solutions under some smallness assumptions imp...
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In this paper, we establish the existence and uniqueness of a time‐periodic solution to the full compressible quantum Euler equations. First, we prove the existence of time‐periodic solutions under some smallness assumptions imposed on the external force in a periodic domain by a regularized approximation scheme and the Leray–Schauder degree theory. Then the result is generalized to ?3 by adapting a limiting method and a diagonal argument. The uniqueness of the time‐periodic solutions is also given. Compared to classical Euler equations, the third‐order quantum spatial derivatives are considered which need some elaborated treatments thereof in obtaining the highest‐order energy estimates.
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We consider the existence of least energy sign-changing (nodal) solutionof Kirchhoff-type elliptic problems with general nonlinearity. Using a truncated technique and constrained minimization on the nodal Nehari manifold, we obtai...
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We consider the existence of least energy sign-changing (nodal) solutionof Kirchhoff-type elliptic problems with general nonlinearity. Using a truncated technique and constrained minimization on the nodal Nehari manifold, we obtain that theKirchhoff-type elliptic problem possesses one least energy sign-changing solution byapplying a Poho?aev type identity. Moreover, the energy of the sign-changing solutionis strictly more than the ground state energy.
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In this paper, we study the following Schr?dinger-Poisson equations,where the parameter λ > 0 and p ∈ (0, 1). When the parameter λ is small and the weight function a(x) fulfills some appropriate conditions, we admit the Schr?di...
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In this paper, we study the following Schr?dinger-Poisson equations,where the parameter λ > 0 and p ∈ (0, 1). When the parameter λ is small and the weight function a(x) fulfills some appropriate conditions, we admit the Schr?dinger-Poisson equations possess infinitely many negative energy solutions by using a truncation technology and applying the usual Krasnoselskii genus theory. In addition, a byproduct is that the set of solutions is compact.
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In this paper, we study the following Schr?dinger-Poisson equations ?Δu+u+?u=u5+λaxup?1u,x∈?3,?Δ?=u2,x∈?3, where the parameter λ>0 and p∈0,1. When the parameter λ is small and the weight function ax fulfills some appropria...
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In this paper, we study the following Schr?dinger-Poisson equations ?Δu+u+?u=u5+λaxup?1u,x∈?3,?Δ?=u2,x∈?3, where the parameter λ>0 and p∈0,1. When the parameter λ is small and the weight function ax fulfills some appropriate conditions, we admit the Schr?dinger-Poisson equations possess infinitely many negative energy solutions by using a truncation technology and applying the usual Krasnoselskii genus theory. In addition, a byproduct is that the set of solutions is compact.
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This paper has investigated the boundedness of a new hyperchaotic Rabinovich system. We have obtained the global exponential attractive set and the ultimate bound Ω_λ for this system. Furthermore, we can conclude that the rate o...
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This paper has investigated the boundedness of a new hyperchaotic Rabinovich system. We have obtained the global exponential attractive set and the ultimate bound Ω_λ for this system. Furthermore, we can conclude that the rate of the trajectories of the system going from the exterior of the set Ω_(λ,2) to the interior of the set Ω_(λ,2) is an exponential rate. The estimate of the trajectories rate is also obtained. Numerical simulations are presented to show the effectiveness of the proposed scheme.
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In this article we consider the Kirchhoff-type elliptic problem where and with if , and otherwise. We show that the problem possesses infinitely many sign-changing solutions by using combination of invariant sets of descent flow a...
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In this article we consider the Kirchhoff-type elliptic problem where and with if , and otherwise. We show that the problem possesses infinitely many sign-changing solutions by using combination of invariant sets of descent flow and the Ljusternik-Schnirelman type minimax method.
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