Results 31 to 40 of about 1,647 (209)
The Lax–Mizohata Theorem for Kirchhoff-Type Equations
Journal of Differential Equations, 2001 The paper deals with the necessity of the hyperbolicity to the Cauchy problem for two types of Kirchhoff equations (abstract Kirchhoff equations and Kirchhoff equations in the classes of real analytic functions) to be locally well-posed. To this end the author uses the gauge invariance of the Kirchhoff-type equations and also some ideas from the ...
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Multiplicity of Solutions for a Modified Schrödinger-Kirchhoff-Type Equation in RN
Discrete Dynamics in Nature and Society, 2015 We study the existence of infinitely many solutions for a class of modified Schrödinger-Kirchhoff-type equations by the dual method and the nonsmooth critical point theory.
Xiumei He
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Infinitely many solutions for the discrete Schrödinger equations with a nonlocal term
Boundary Value Problems, 2022 In the present paper, we consider the following discrete Schrödinger equations − ( a + b ∑ k ∈ Z | Δ u k − 1 | 2 ) Δ 2 u k − 1 + V k u k = f k ( u k ) k ∈ Z , $$ - \biggl(a+b\sum_{k\in \mathbf{Z}} \vert \Delta u_{k-1} \vert ^{2} \biggr) \Delta ^{2} u_{k ...
Qilin Xie, Huafeng Xiao
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Critical Kirchhoff equations involving the -sub-Laplacians operators on the Heisenberg group
Bulletin of Mathematical Sciences, 2023 In this paper, we deal with a class of Kirchhoff-type critical elliptic equations involving the [Formula: see text]-sub-Laplacians operators on the Heisenberg group of the form M(∥DHu∥pp + ∥u∥ p,Vp)[−Δ H,pu + V (ξ)|u|p−2u] = λf(ξ,u) + |u|p∗−2u,ξ ∈ ℍn,u ...
Xueqi Sun +3 more
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Advanced Functional Materials, EarlyView.An all‐in‐one analog AI accelerator is presented, enabling on‐chip training, weight retention, and long‐term inference acceleration. It leverages a BEOL‐integrated CMO/HfOx ReRAM array with low‐voltage operation (<1.5 V), multi‐bit capability over 32 states, low programming noise (10 nS), and near‐ideal weight transfer.
Donato Francesco Falcone +11 more
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Global Attractors of the Extensible Plate Equations with Nonlinear Damping and Memory
Journal of Function Spaces, 2017 We prove in this paper the existence of a global attractor for the plate equations of Kirchhoff type with nonlinear damping and memory using the contraction function method.
Xiaobin Yao, Qiaozhen Ma
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Multiple Solutions to a Non-Local Problem of Schrödinger–Kirchhoff Type in ℝN
Fractal and Fractional, 2023 The main purpose of this paper is to show the existence of a sequence of infinitely many small energy solutions to the nonlinear elliptic equations of Kirchhoff–Schrödinger type involving the fractional p-Laplacian by employing the dual fountain theorem ...
In Hyoun Kim, Yun-Ho Kim, Kisoeb Park
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Advanced Functional Materials, EarlyView.Metasurfaces and other structured photonic environments can dramatically modify the absorption and/or light emission of semiconductors. However, the consequences of these changes on the temperature of the system are not well understood. The authors address this problem for colloidal nanocrystals and leverage their findings to convert light into ...
Hugo Kowalczyk +7 more
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Scattering for a Quasilinear Hyperbolic Equation of Kirchhoff Type
Journal of Differential Equations, 1998 The global solvability and the existence of the scattering operator for the quasilinear hyperbolic Kirchhoff type equation \[ {\partial^2 u\over \partial t^2}= m\bigl( \| \nabla u\|^2 \bigr)^2 \Delta u\quad \text{in} \quad \mathbb{R}^n_x \times \mathbb{R}_t \tag{1} \] \[ u(x,0) =\varphi_0 (x),\quad {\partial u\over \partial t} (x,0)= \psi_0 (x) \tag{2}
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Concentration phenomena for a fractional Schrödinger‐Kirchhoff type equation
Mathematical Methods in the Applied Sciences, 2017 In this paper, we deal with the multiplicity and concentration of positive solutions for the following fractional Schrödinger‐Kirchhoff type equation urn:x-wiley:mma:media:mma4633:mma4633-math-0001 where ε>0 is a small parameter, is the fractional Laplacian, M is a Kirchhoff function, V is a continuous positive potential, and f is a superlinear ...
Vincenzo Ambrosio, Teresa Isernia
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