Results 71 to 80 of about 2,094 (218)

A New Result Concerning the Solvability of a Class of General Systems of Variational Equations with Nonmonotone Operators: Applications to Dirichlet and Neumann Nonlinear Problems

International Journal of Differential Equations, 2016
A new result of solvability for a wide class of systems of variational equations depending on parameters and governed by nonmonotone operators is found in a Banach real and reflexive space with applications to Dirichlet and Neumann problems related to ...
Luisa Toscano, Speranza Toscano
doaj   +1 more source

RAMS: Residual‐Based Adversarial‐Gradient Moving Sample Method for Scientific Machine Learning in Solving Partial Differential Equations

Advanced Intelligent Discovery, Volume 2, Issue 3, June 2026.
We propose a residual‐based adversarial‐gradient moving sample (RAMS) method for scientific machine learning that treats samples as trainable variables and updates them to maximize the physics residual, thereby effectively concentrating samples in inadequately learned regions.
Weihang Ouyang, Min Zhu, Wei Xiong, Si‐Wei Liu, Lu Lu   +4 more
wiley   +1 more source

Derivative free processes of high order for nondifferentiable equations in Banach spaces [PDF]

[EN] In this article, we consider two parametric classes of derivative free iterative methods of high order of convergence in Banach spaces. We study local and semilocal convergence results in Banach spaces for both families of iterative processes.
Villalba, Eva G. [0000-0003-1357-8410], Martínez, Eulalia [0000-0003-2869-4334], Argyros, Ioannis K., Hernández-Verón, null [0000-0001-5478-2958], Villalba, Eva G., Hernández-Verón, M. A., Martínez Molada, Eulalia   +6 more
core   +1 more source

The fixed point theorem and the boundedness of solutions of differential equations in the Banach space [PDF]

, 1993
summary:The properties of solutions of the nonlinear differential equation $x'=A(s)x+f(s,x)$ in a Banach space and of the special case of the homogeneous linear differential equation $x'=A(s)x$ are studied.
Tumajer, František
core   +1 more source

Long‐Time Solvability and Asymptotics for the 3D Rotating MHD Equations

Mathematische Nachrichten, Volume 299, Issue 6, Page 1480-1509, June 2026.
ABSTRACT We consider the initial value problem for the 3D incompressible rotating MHD equations around a constant magnetic field. We prove the long‐time existence and uniqueness of solutions for small viscosity coefficient and high rotating speed. Moreover, we investigate the asymptotic behavior of solutions in the limit of vanishing viscosity and fast
Hiroki Ohyama
wiley   +1 more source

An exponentially convergent algorithm for nonlinear differential equations in Banach spaces [PDF]

Mathematics of Computation, 2007
An exponentially convergent approximation to the solution of a nonlinear first order differential equation with an operator coefficient in Banach space is proposed. The algorithm is based on an equivalent Volterra integral equation including the operator exponential generated by the operator coefficient.
Ivan P. Gavrilyuk, Volodymyr L. Makarov
openaire   +1 more source

Asymptotic behaviour of mild solution of nonlinear stochastic partial functional equations

, 2019
This paper presents conditions to assure existence, uniqueness and stability for impulsive neutral stochastic integrodifferential equations with delay driven by Rosenblatt process and Poisson jumps.
Ogouyandjou, Carlos, Diop, Mamadou Abdoul Abdoul, Sakthivel, Rathinasamy, Gbaguidi Amoussou, Amour Toffodji Toffodji   +3 more
core   +1 more source

From Stability to Chaos: A Complete Classification of the Damped Klein‐Gordon Dynamics

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9696-9708, June 2026.
ABSTRACT We investigate the transition between stability and chaos in the damped Klein‐Gordon equation, a fundamental model for wave propagation and energy dissipation. Using semigroup methods and spectral criteria, we derive explicit thresholds that determine when the system exhibits asymptotic stability and when it displays strong chaotic dynamics ...
Carlos Lizama, Marina Murillo‐Arcila, Julio Puerta‐Fernández   +2 more
wiley   +1 more source

Nonlinear differential equations in reflexive Banach spaces [PDF]

Bulletin of the Australian Mathematical Society, 1974
Let X be a reflexive Banach space and be a family of weakly continuous operators which map X to X. Conditions are provided which guarantee the existence and the uniqueness to the Cauchy initial value problem
openaire   +2 more sources

Matsumura‐Type Estimates and Global Solutions of a Fractional Wave Equation With Nonlocal Nonlinearity

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9967-9983, June 2026.
ABSTRACT The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of εutt+ut+(−Δ)βu=0,u(0,x)=φ(x),ut(0,x)=ψ(x),$$ \varepsilon {u}_{tt}+{u}_t+{\left(-\Delta \right)}^{\beta }u=0,\kern1em u ...
Ibrahim Ahmad Suleman, Mokhtar Kirane
wiley   +1 more source