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We consider a wide class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously differentiable…

Classical Analysis and ODEs · Mathematics 2020-11-24 Hanna Masliuk , Olha Pelekhata , Vitalii Soldatov

In this article we will investigate the large time behavior of solutions of a special class of initial/boundary value problems that involve nonlinear damped beam equations. We will show that the solution energies of global pseudo classical…

Analysis of PDEs · Mathematics 2025-11-04 David Raske

We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…

Dynamical Systems · Mathematics 2023-04-13 Svetlin Georgiev , Sergey Kryzhevich

A new boundary value problem for partial differential equations is discussed. We consider an arbitrary solution of an elliptic or parabolic equation in a given domain and no boundary conditions are assumed. We study which restrictions the…

Analysis of PDEs · Mathematics 2013-12-17 V. Zh. Sakbaev , I. V. Volovich

We prove conditions for existence of analytical solutions for boundary value problems with the Hilfer fractional derivative, generalizing the commonly used Riemann-Liouville and Caputo operators. The boundary values, referred to in this…

Numerical Analysis · Mathematics 2026-01-21 Niels Goedegebure , Kateryna Marynets

In this work, we consider a generalization of the nonlinear Langevin equation of fractional orders with boundary value conditions. The existence and uniqueness of solutions are studied by using results of the fixed point theory. Moreover,…

Analysis of PDEs · Mathematics 2020-04-08 Saeed Kosari , Milad Yadollahzadeh , Zehui Shao , Yongsheng Rao

We prove global existence and blow-up of solutions of initial-boundary value problem for nonlinear nonlocal parabolic equation with nonlinear nonlocal boundary condition. Obtained results depend on the behavior of variable coefficients for…

Analysis of PDEs · Mathematics 2020-05-20 Alexander Gladkov , Tatiana Kavitova

In this paper, we consider the initial boundary value problem of a doubly nonlinear parabolic equation with nonlinear perturbation. We impose the homogeneous Dirichlet condition on this problem. We aim to reduce the growth condition of the…

Analysis of PDEs · Mathematics 2025-06-16 Shun Uchida

A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…

Classical Analysis and ODEs · Mathematics 2010-01-29 N. S. Hoang , A. G. Ramm

In this paper there are estimated the derivatives of the solution of an initial boundary value problem for a nonlinear uniformly parabolic equation in the interior with the total variation of the boundary data and the L^{infinity}-norm of…

Analysis of PDEs · Mathematics 2007-05-23 Giuseppe Maria Coclite

Using the theory of fixed point index, we discuss the existence and multiplicity of non-negative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a…

Classical Analysis and ODEs · Mathematics 2014-08-14 Gennaro Infante , Paolamaria Pietramala

In this paper we are concerned with the initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains in spatial-temporal space. We obtain the existence of a weak…

Analysis of PDEs · Mathematics 2016-11-22 Tujin Kim , Daomin Cao

The boundary value problems for linear and nonlinear singular degenerate differential-operator equations are studied. We prove a well-posedeness of linear problem and optimal regularity result for the nonlinear problem which occur in fluid…

Analysis of PDEs · Mathematics 2017-07-06 Veli Shakhmurov

In this paper, we investigate the existence and uniqueness of solutions for a fractional boundary value problem supplemented with nonlocal Riemann-Liouville fractional integral and Caputo fractional derivative boundary conditions. Our…

Classical Analysis and ODEs · Mathematics 2018-05-17 Faouzi Haddouchi

We revisit a textbook example of a singularly perturbed nonlinear boundary-value problem. Unexpectedly, it shows a wealth of phenomena that seem to have been overlooked previously, including a pitchfork bifurcation in the number of…

Classical Analysis and ODEs · Mathematics 2023-02-13 William A. Clark , Mario W. Gomes , Arnaldo Rodriguez-Gonzalez , Leo C. Stein , Steven H. Strogatz

We study the most general class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the complex H\"older space $C^{n+r,\alpha}$, with $0\leq n\in\mathbb{Z}$ and…

Classical Analysis and ODEs · Mathematics 2020-05-05 Hanna Masliuk , Vitalii Soldatov

This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…

Linearisation is often used as a first step in the analysis of nonlinear initial boundary value problems. The linearisation procedure frequently results in a confusing contradiction where the nonlinear problem conserves energy and has an…

Numerical Analysis · Mathematics 2024-12-31 Jan Nordström

We study existence of solutions for a boundary degenerate (or singular) quasilinear equation in a smooth bounded domain under Dirichlet boundary conditions. We consider a weighted $p-${L}aplacian operator with a coefficient that is {locally…

Analysis of PDEs · Mathematics 2021-02-10 Oscar Agudelo , Pavel Drábek

In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].

Complex Variables · Mathematics 2022-02-09 Garima Pant , Manisha Saini