共查询到20条相似文献,搜索用时 31 毫秒
1.
Jiabin Zuo Tianqing An Alessio Fiscella 《Mathematical Methods in the Applied Sciences》2021,44(1):1071-1085
The paper deals with the following Kirchhoff‐type problem where M models a Kirchhoff coefficient, is a variable s(·) ‐order p(·) ‐fractional Laplace operator, with and . Here, is a bounded smooth domain with N > p(x, y)s(x, y) for any , μ is a positive parameter, g is a continuous and subcritical function, while variable exponent r(x) could be close to the critical exponent , given with and for . We prove the existence and asymptotic behavior of at least one non‐trivial solution. For this, we exploit a suitable tricky step analysis of the critical mountain pass level, combined with a Brézis and Lieb‐type lemma for fractional Sobolev spaces with variable order and variable exponent. 相似文献
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In this paper, we study the existence of ground state solutions for the modified fractional Schrödinger equations where , , , and are positive parameters, , denotes the fractional Laplacian of order . For the case and the case , the existence results of ground state solutions are given, respectively. 相似文献
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In this paper, we concern with the following fractional p‐Laplacian equation with critical Sobolev exponent where ε > 0 is a small parameter, λ > 0 , N is a positive integer, and N > ps with s ∈ (0, 1) fixed, . Since the nonlinearity does not satisfy the following Ambrosetti‐Rabinowitz condition: with μ > p , it is difficult to obtain the boundedness of Palais‐Smale sequence, which is important to prove the existence of positive solutions. In order to overcome the above difficulty, we introduce a penalization method of fractional p‐Laplacian type. 相似文献
4.
We provide a characterization for the existence and uniqueness of solutions in the space of vector‐valued sequences for the multiterm fractional delayed model in the form where X is a Banach space, A is a closed linear operator with domain D(A) defined on X, and ΔΓ denotes the Grünwald–Letkinov fractional derivative of order Γ > 0. We also give some conditions to ensure the existence of solutions when adding nonlinearities. Finally, we illustrate our results with an example given by a general abstract nonlinear model that includes the fractional Fisher equation with delay. 相似文献
5.
Yujun Liu 《Mathematical Methods in the Applied Sciences》2020,43(5):2491-2515
This paper focuses on the 2D incompressible magneto-micropolar sysytem with the kinematic dissipation given by the fractional operator (−Δ)α, the magnetic diffusion by the fractional operator (−Δ)β and the spin dissipation by the fractional operator (−Δ)γ. α,β, and γ are nonnegative constants. We proved that this system with any α+β=2,1 ≤ α ≤ 2,γ=0, and α+γ ≥ 1,β=1 always possesses a unique global smooth solution if the initial data is sufficiently smooth. In addition, we also obtained the global regularity results for several partial dissipation cases. 相似文献
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This article examines the existence and uniqueness of weak solutions to the d‐dimensional micropolar equations (d=2 or d=3) with general fractional dissipation (?Δ)αu and (?Δ)βw. The micropolar equations with standard Laplacian dissipation model fluids with microstructure. The generalization to include fractional dissipation allows simultaneous study of a family of equations and is relevant in some physical circumstances. We establish that, when and , any initial data (u0,w0) in the critical Besov space and yields a unique weak solution. For α ≥ 1 and β=0, any initial data and also leads to a unique weak solution as well. The regularity indices in these Besov spaces appear to be optimal and can not be lowered in order to achieve the uniqueness. Especially, the 2D micropolar equations with the standard Laplacian dissipation, namely, α=β=1, have a unique weak solution for . The proof involves the construction of successive approximation sequences and extensive a priori estimates in Besov space settings. 相似文献
8.
Nelson Faustino 《Mathematische Nachrichten》2023,296(7):2758-2779
In this paper, we introduce a wide class of space-fractional and time-fractional semidiscrete Dirac operators of Lévy–Leblond type on the semidiscrete space-time lattice (), resembling to fractional semidiscrete counterparts of the so-called parabolic Dirac operators. The methods adopted here are fairly operational, relying mostly on the algebraic manipulations involving Clifford algebras, discrete Fourier analysis techniques as well as standard properties of the analytic fractional semidiscrete semigroup , carrying the parameter constraints and . The results obtained involve the study of Cauchy problems on . 相似文献
9.
In the paper mentioned in the title, it is proved the boundedness of the Riesz potential operator of variable order α(x) from variable exponent Morrey space to variable exponent Campanato space, under certain assumptions on the variable exponents p(x) and λ(x) of the Morrey space. Assumptions on the exponents were different depending on whether takes or not the critical values 0 or 1. In this note, we improve those results by unifying all the cases and covering the whole range . We also provide a correction to some minor technicality in the proof of Theorem 2 in the aforementioned paper. 相似文献
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In this paper, we study the following Schrödinger-Poisson equations: where , is a parameter and and satisfy the critical frequency conditions. By using variational methods and penalization arguments, we show the existence of multibump solutions for the above system. Furthermore, the heights of these bumps are different order. 相似文献
12.
In this article, we study the blow‐up of the damped wave equation in the scale‐invariant case and in the presence of two nonlinearities. More precisely, we consider the following equation: with small initial data. For and μ ∈ (0, μ?) , where μ? > 0 is depending on the nonlinearties' powers and the space dimension (μ? satisfies ), we prove that the wave equation, in this case, behaves like the one without dissipation (μ = 0 ). Our result completes the previous studies in the case where the dissipation is given by , where, contrary to what we obtain in the present work, the effect of the damping is not significant in the dynamics. Interestingly, in our case, the influence of the damping term is important. 相似文献
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In this paper, we mainly study the local energy equation of the weak solutions of the compressible isentropic MHD equation defined on . We prove that the regularity of the solution is sufficient to guarantee the balance of the total energy in the space. We adopt a variant of the method of Feireisl et al. 相似文献
15.
Anh Tuan Duong Tran Thi Loan Dao Trong Quyet Dao Manh Thang 《Mathematische Nachrichten》2023,296(6):2321-2331
In this paper, we are concerned with the fractional Choquard equation on the whole space with , and . We first prove that the equation does not possess any positive solution for . When , we establish a Liouville type theorem saying that if then the equation has no positive stable solution. This extends, in particular, a result in [27] to the fractional Choquard equation. 相似文献
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Rong Yin Jihui Zhang Xudong Shang 《Mathematical Methods in the Applied Sciences》2020,43(15):8736-8752
This paper is dedicated to studying the following Schrödinger–Poisson system Under some different assumptions on functions V(x), K(x), a(x) and f(u), by using the variational approach, we establish the existence of positive ground state solutions. 相似文献
18.
Nguyen Anh Triet Le Thi Phuong Ngoc Alain Pham Ngoc Dinh Nguyen Thanh Long 《Mathematical Methods in the Applied Sciences》2021,44(1):668-692
This paper is devoted to the study of a nonlinear wave equation with initial conditions and nonlocal boundary conditions of 2N‐point type, which connect the values of an unknown function u(x,t) at x = 1, x = 0, x = ηi(t) , and x = θi(t), where for all t ≥ 0. First, we prove local existence of a unique weak solution by using density arguments and applying the Banach's contraction principle. Next, under the suitable conditions, we show that the problem considered has a unique global solution u(t) with energy decaying exponentially as t → +∞ . Finally, we present numerical results. 相似文献
19.
Britta Schmitt Boris N. Khoromskij Venera Khoromskaia Volker Schulz 《Numerical Linear Algebra with Applications》2022,29(1):e2404
We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional two- (2D) and three-dimensional (3D) elliptic operators with variable coefficients. We solve the governing equation for the control function which includes a sum of the fractional operator and its inverse, both discretized over large 3D spacial grids. Using the diagonalization of the arising matrix-valued functions in the eigenbasis of the one-dimensional Sturm–Liouville operators, we construct the rank-structured tensor approximation with controllable precision for the discretized fractional elliptic operators and the respective preconditioner. The right-hand side in the constraining equation (the optimal design function) is supposed to be represented in a form of a low-rank canonical tensor. Then the equation for the control function is solved in a tensor structured format by using preconditioned CG iteration with the adaptive rank truncation procedure that also ensures the accuracy of calculations, given an -threshold. This method reduces the numerical cost for solving the control problem to (plus the quadratic term with a small weight), which outperforms traditional approaches with complexity in the 3D case. The storage for the representation of all 3D nonlocal operators and functions involved is also estimated by . This essentially outperforms the traditional methods operating with fully populated matrices and vectors in . Numerical tests for 2D/3D control problems indicate the almost linear complexity scaling of the rank truncated preconditioned conjugate gradient iteration in the univariate grid size n. 相似文献
20.
Stevo Stevi 《Mathematical Methods in the Applied Sciences》2022,45(1):546-556
We investigate the following multilinear integral operator where and is a continuous kernel function satisfying the condition for some functions , which are continuous, increasing, , and a function , from a product of weighted-type spaces to weighted-type spaces of real functions. We calculate the norm of the operator, extending and complementing some results in the literature. We also give an explanation for a relation between integrals of an Lp integrable function and its radialization on . 相似文献