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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Jia‐Feng Liao 《Mathematical Methods in the Applied Sciences》2021,44(1):407-418
In this article, we devote ourselves to investigate the following singular Kirchhoff‐type equation: where is a bounded domain with smooth boundary ?Ω,0∈Ω,a≥0,b,λ>0,0<γ,s<1, and By using the variational and perturbation methods, we obtain the existence of two positive solutions, which generalizes and improves the recent results in the literature. 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 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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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
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Ferenc Weisz 《Mathematische Nachrichten》2023,296(4):1687-1705
Let be a measurable function defined on and . In this paper, we generalize the Hardy–Littlewood maximal operator. In the definition, instead of cubes or balls, we take the supremum over all rectangles the side lengths of which are in a cone-like set defined by a given function ψ. Moreover, instead of the integral means, we consider the -means. Let and satisfy the log-Hülder condition and . Then, we prove that the maximal operator is bounded on if and is bounded from to the weak if . We generalize also the theorem about the Lebesgue points. 相似文献
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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
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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
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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
10.
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
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Hiroyuki Tsurumi 《Mathematische Nachrichten》2023,296(4):1651-1668
We consider the stationary Navier–Stokes equations in the two-dimensional torus . For any , we show the existence, uniqueness, and continuous dependence of solutions in homogeneous toroidal Besov spaces for given small external forces in when . These spaces become closer to the scaling invariant ones if the difference ε becomes smaller. This well-posedness is proved by using the embedding property and the para-product estimate in homogeneous Besov spaces. In addition, for the case , we can show the ill-posedness, even in the scaling invariant spaces. Actually in such cases of p and q, we can prove that ill-posedness by showing the discontinuity of a certain solution map from to . 相似文献
13.
We are concerned with the following Choquard equation: where , , , , is the p-Laplacian, is the Riesz potential, and F is the primitive of f which is of critical growth due to the Hardy–Littlewood–Sobolev inequality. Under different range of θ and almost necessary conditions on the nonlinearity f in the spirit of Berestycki–Lions-type conditions, we divide this paper into three parts. By applying the refined Sobolev inequality with Morrey norm and the generalized version of the Lions-type theorem, some existence results are established. It is worth noting that our method is not involving the concentration–compactness principle. 相似文献
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For and variable exponents and with values in [1, ∞], let the variable exponents be defined by The Riesz–Thorin–type interpolation theorem for variable Lebesgue spaces says that if a linear operator T acts boundedly from the variable Lebesgue space to the variable Lebesgue space for , then where C is an interpolation constant independent of T. We consider two different modulars and generating variable Lebesgue spaces and give upper estimates for the corresponding interpolation constants Cmax and Csum, which imply that and , as well as, lead to sufficient conditions for and . We also construct an example showing that, in many cases, our upper estimates are sharp and the interpolation constant is greater than one, even if one requires that , are Lipschitz continuous and bounded away from one and infinity (in this case, ). 相似文献
16.
Tomoyuki Nakatsuka 《Mathematische Nachrichten》2021,294(1):98-117
We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution of the Navier–Stokes equation such that and uniformly in as . Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described. 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
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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