Results 71 to 80 of about 2,989,822 (277)
Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
wiley +1 more source
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT It is an elementary fact in the scientific literature that the Lipschitz norm of the realization function of a feedforward fully connected rectified linear unit (ReLU) artificial neural network (ANN) can, up to a multiplicative constant, be bounded from above by sums of powers of the norm of the ANN parameter vector.
Arnulf Jentzen, Timo Kröger
wiley +1 more source
Multiple Solutions for a Class of Differential Inclusion System Involving the (p(x),q(x))-Laplacian
Abstract and Applied Analysis, 2012 We consider a differential inclusion system involving the (p(x),q(x))-Laplacian with Dirichlet boundary condition on a bounded domain and obtain two nontrivial solutions under appropriate hypotheses.
Bin Ge, Ji-Hong Shen
doaj +1 more source
An inverse problem of Calderon type with partial data [PDF]
, 2011 A generalized variant of the Calder\'on problem from electrical impedance tomography with partial data for anisotropic Lipschitz conductivities is considered in an arbitrary space dimension $n \geq 2$.
Behrndt, Jussi, Rohleder, Jonathan
core
Improved upper bounds for the Hot Spots constant of Lipschitz domains [PDF]
, 2021 Phanuel Mariano, Hugo Panzo, Jing Wang
openalex +1 more source
Safe global optimization of expensive noisy black-box functions in the $δ$-Lipschitz framework [PDF]
Soft Computing - A Fusion of Foundations, Methodologies and Applications, 2019 In this paper, the problem of safe global maximization (it should not be confused with robust optimization) of expensive noisy black-box functions satisfying the Lipschitz condition is considered.
Y. Sergeyev +3 more
semanticscholar +1 more source
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT The article examines a boundary‐value problem in a bounded domain Ωε$$ {\Omega}_{\varepsilon } $$ consisting of perforated and imperforate regions, with Neumann conditions prescribed at the boundaries of the perforations. Assuming the porous medium has symmetric, periodic structure with a small period ε$$ \varepsilon $$, we analyze the limit ...
Taras Melnyk
wiley +1 more source
Asymptotics for the Spectrum of the Laplacian in Thin Bars with Varying Cross Sections
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We consider spectral problems for the Laplace operator in 3D rod structures with a small cross section of diameter O(ε)$$ O\left(\varepsilon \right) $$, ε$$ \varepsilon $$ being a positive parameter. The boundary conditions are Dirichlet (Neumann, respectively) on the bases of this structure, and Neumann on the lateral boundary.
Pablo Benavent‐Ocejo +2 more
wiley +1 more source
Existence Analysis of a Three‐Species Memristor Drift‐Diffusion System Coupled to Electric Networks
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT The existence of global weak solutions to a partial‐differential‐algebraic system is proved. The system consists of the drift‐diffusion equations for the electron, hole, and oxide vacancy densities in a memristor device, the Poisson equation for the electric potential, and the differential‐algebraic equations for an electric network.
Ansgar Jüngel, Tuấn Tùng Nguyến
wiley +1 more source
, 2014 This article investigates how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain in the case when the domains involved are of class $C^1$.
Thim, Johan
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