共查询到20条相似文献,搜索用时 656 毫秒
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Shurong Sun Yige Zhao Zhenlai Han Yanan Li 《Communications in Nonlinear Science & Numerical Simulation》2012,17(12):4961-4967
In this paper, we study the existence of solutions for the boundary value problem of fractional hybrid differential equationswhere is a real number, is the Riemann–Liouville fractional derivative. By a fixed point theorem in Banach algebra due to Dhage, an existence theorem for fractional hybrid differential equations is proved under mixed Lipschitz and Carathéodory conditions. As an application, examples are presented to illustrate the main results. 相似文献
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In this paper, we study the following fractional Kirchhoff equations where are constants, and is the fractional Laplacian operator with , , , is real parameter. is the critical Sobolev exponent. g satisfies the Berestycki–Lions-type condition (see [2]). By using Poho?aev identity and concentration-compact theory, we show that the above problem has at least one nontrivial solution. Furthermore, the phenomenon of concentration of solutions is also explored. Our result supplements the results of Lü (see [8]) concerning the Hartree-type nonlinearity with . 相似文献
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Matías G. Delgadino Scott Smith 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(3):577-604
This work focuses on drift-diffusion equations with fractional dissipation in the regime . Our main result is an a priori Hölder estimate on smooth solutions to the Cauchy problem, starting from initial data with finite energy. We prove that for some , the norm of the solution depends only on the size of the drift in critical spaces of the form with and , along with the norm of the initial datum. The proof uses the Caffarelli/Vasseur variant of De Giorgi's method for non-local equations. 相似文献
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Wright's conjecture states that the origin is the global attractor for the delay differential equation for all when . This has been proven to be true for a subset of parameter values α. We extend the result to the full parameter range , and thus prove Wright's conjecture to be true. Our approach relies on a careful investigation of the neighborhood of the Hopf bifurcation occurring at . This analysis fills the gap left by complementary work on Wright's conjecture, which covers parameter values further away from the bifurcation point. Furthermore, we show that the branch of (slowly oscillating) periodic orbits originating from this Hopf bifurcation does not have any subsequent bifurcations (and in particular no folds) for . When combined with other results, this proves that the branch of slowly oscillating solutions that originates from the Hopf bifurcation at is globally parametrized by . 相似文献
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Fritz Gesztesy Lance L. Littlejohn Isaac Michael Richard Wellman 《Journal of Differential Equations》2018,264(4):2761-2801
In 1961, Birman proved a sequence of inequalities , for , valid for functions in . In particular, is the classical (integral) Hardy inequality and is the well-known Rellich inequality. In this paper, we give a proof of this sequence of inequalities valid on a certain Hilbert space of functions defined on . Moreover, implies ; as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman's sequence. We also show that for any finite , these inequalities hold on the standard Sobolev space . Furthermore, in all cases, the Birman constants in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in (resp., ). We also show that these Birman constants are related to the norm of a generalized continuous Cesàro averaging operator whose spectral properties we determine in detail. 相似文献
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《Journal of Computational and Applied Mathematics》2006,188(1):65-76
The number of zeros in of the Jacobi function of second kind , , i.e. the second solution of the differential equationis determined for every and for all values of the parameters and . It turns out that this number depends essentially on and as well as on the specific normalization of the function . Interlacing properties of the zeros are also obtained. As a consequence of the main result, we determine the number of zeros of Laguerre's and Hermite's functions of second kind. 相似文献
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《Nonlinear Analysis: Real World Applications》2007,8(4):1062-1078
This paper deals with the existence and nonexistence of nonconstant positive steady-state solutions to a ratio-dependent predator–prey model with diffusion and with the homogeneous Neumann boundary condition. We demonstrate that there exists satisfying for , such that if and , then the diffusion can create nonconstant positive steady-state solutions; whereas the diffusion cannot do provided . 相似文献
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Given , a compact connected Riemannian manifold of dimension , with boundary ?M, we consider an initial boundary value problem for a fractional diffusion equation on , , with time-fractional Caputo derivative of order . We prove uniqueness in the inverse problem of determining the smooth manifold (up to an isometry), and various time-independent smooth coefficients appearing in this equation, from measurements of the solutions on a subset of ?M at fixed time. In the “flat” case where M is a compact subset of , two out the three coefficients ρ (density), a (conductivity) and q (potential) appearing in the equation on are recovered simultaneously. 相似文献