Results 51 to 60 of about 41,256 (237)

Exact solutions and bifurcation curves of nonlocal elliptic equations with convolutional Kirchhoff functions

Boundary Value Problems
We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with convolutional Kirchhoff functions. We establish the exact solutions u λ $u_{\lambda}$ and bifurcation curves λ ( α ) $\lambda (\alpha )$ , where α : = ∥ u λ ∥ ∞ $\alpha ...
Tetsutaro Shibata
doaj   +1 more source

Asymptotic Limits for Mildly Degenerate Kirchhoff Equations [PDF]

SIAM Journal on Mathematical Analysis, 2013
We study the asymptotic behavior of the solutions of the mildly degenerate Kirchhoff equation with a dissipative term. We obtain a new estimate on second-in-time derivative of the solution. Moreover we renormalize the solution in such a way that the renormalization as a no zero limit as t goes to infinity.
openaire   +3 more sources

Optimal Control of the Kirchhoff Equation

, 2021
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the state equation, existence of global optimal solutions, differentiability of the control-to-state map and first-order ...
Hashemi, Masoumeh, Herzog, Roland, Surowiec, Thomas M.   +2 more
openaire   +2 more sources

Topology and Material Optimization in Ultra‐Soft Magneto‐Active Structures: Making Advantage of Residual Anisotropies

Advanced Materials, EarlyView.
Residual magnetization induces pronounced mechanical anisotropy in ultra‐soft magnetorheological elastomers, shaping deformation and actuation even without external magnetic fields. This study introduces a computational‐experimental framework integrating magneto‐mechanical coupling into topology optimization for designing soft magnetic actuators with ...
Carlos Perez‐Garcia, Rogelio Ortigosa, Jesús Martínez‐Frutos, Daniel Garcia‐Gonzalez   +3 more
wiley   +1 more source

A class of p1(x, ⋅) & p2(x, ⋅)-fractional Kirchhoff-type problem with variable s(x, ⋅)-order and without the Ambrosetti-Rabinowitz condition in ℝN

Open Mathematics, 2022
In this article, we study a class of Kirchhoff-type equation driven by the variable s(x, ⋅)-order fractional p1(x, ⋅) & p2(x, ⋅)-Laplacian. With the help of three different critical point theories, we obtain the existence and multiplicity of solutions in
Bu Weichun, An Tianqing, Zuo Jiabin
doaj   +1 more source

Bilinear boundary optimal control of a Kirchhoff plate equation

Results in Control and Optimization, 2022
This work shows that a problem of boundary optimal control of a Kirchhoff plate equation has a solution that we characterized using the differentiability of a functional cost.
Abdelhak Bouhamed, Abella El kabouss, Hassane Bouzahir   +2 more
doaj   +1 more source

Multiple critical points for a class of nonlinear functionals

, 2010
In this paper we prove a multiplicity result concerning the critical points of a class of functionals involving local and nonlocal nonlinearities. We apply our result to the nonlinear Schrodinger-Maxwell system and to the nonlinear elliptic Kirchhoff ...
Azzollini, Antonio, d'Avenia, Pietro, Pomponio, Alessio   +2 more
core   +1 more source

Neuromorphic Electronics for Intelligence Everywhere: Emerging Devices, Flexible Platforms, and Scalable System Architectures

Advanced Materials, EarlyView.
The perspective presents an integrated view of neuromorphic technologies, from device physics to real‐time applicability, while highlighting the necessity of full‐stack co‐optimization. By outlining practical hardware‐level strategies to exploit device behavior and mitigate non‐idealities, it shows pathways for building efficient, scalable, and ...
Kapil Bhardwaj, Roshni Satheesh Babu, Yuxin Xia, Eva Bestelink, Radu Sporea, Nikos Hastas, Ioannis Zeimpekis, Dimitra G. Georgiadou, Sayani Majumdar   +8 more
wiley   +1 more source

Existence of Strictly Positive Solutions for a Kirchhoff-Type Equation with the Dirichlet Boundary on Locally Finite Graphs

Axioms
In this paper, we investigate the existence of multiple solutions for a Kirchhoff-type equation with Dirichlet boundary conditions defined on locally finite graphs.
Yanhong Li, Xingyong Zhang
doaj   +1 more source

Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations

Advances in Nonlinear Analysis, 2016
The purpose of this paper is mainly to investigate the existence of entire solutions of the stationary Kirchhoff type equations driven by the fractional p-Laplacian operator in ℝN.
Pucci Patrizia, Xiang Mingqi, Zhang Binlin   +2 more
doaj   +1 more source