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We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…

Dynamical Systems · Mathematics 2013-06-12 A. Gorban , I. Tyukin , E. Steur , H. Nijmeijer

Let Omega be a bounded, simply connected domain with boundary of class C^{1,1} except at finitely many points S_j where the boundary is locally a corner of aperture alpha_j<=pi/2. Improving on results of Grisvard, we show that the solution…

Analysis of PDEs · Mathematics 2013-10-22 Francesco Di Plinio , Roger Temam

In this paper we study the nonlinear Neumann boundary value problem of the following equations -\text{div}(|\nabla u|^{p_{1}(x)-2}\nabla u)-\text{div}(|\nabla u|^{p_{2}(x)-2}\nabla u)+|u|^{p_{1}(x)-2}u+|u|^{p_{2}(x)-2}u=\lambda f(x,u) in a…

Analysis of PDEs · Mathematics 2012-05-17 Duchao Liu , Xiaoyan Wang , Jinghua Yao

In this paper we will discuss the Dirichlet problem of nonlinear second order partial differential equations resolved with any derivatives. First, we transform it into generalized integral equations. Next, we discuss the existence of the…

General Mathematics · Mathematics 2024-05-23 Jianfeng Wang

Several different problems make the study of the so called Lyapunov type inequalities of great interest, both in pure and applied mathematics. Although the original historical motivation was the study of the stability properties of the Hill…

Analysis of PDEs · Mathematics 2011-10-06 Antonio Canada , Salvador Villegas

In this paper, we deal with a Cauchy problem for a nonlinear fractional differential equation with the Caputo derivative of order $\alpha \in (0, 1)$. As initial data, we consider a pair consisting of an initial point, which does not…

Optimization and Control · Mathematics 2022-08-23 Mikhail I. Gomoyunov

In this paper we analyse some possibilities of finding positive solutions for second order boundary value problems with Dirichlet and periodic boundary conditions, for which the correspondent Green's functions change sign. The obtained…

Classical Analysis and ODEs · Mathematics 2017-06-23 Alberto Cabada , Ricardo Enguiça , Lucía López-Somoza

Using direct variational method we consider the existence of non-spurious solutions to the following Dirichlet problem $\ddot{x}\left( t\right) =f\left( t,x\left( t\right) \right) $, $x\left( 0\right) =x\left( 1\right) =0 $ where $f:\left[…

Classical Analysis and ODEs · Mathematics 2015-03-09 Marek Galewski , Ewa Schmeidel

In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra…

Classical Analysis and ODEs · Mathematics 2022-03-23 A. Sinan Ozkan , İbrahim Adalar

This paper investigates the existence of positive solutions for m-point p-Laplacian fractional boundary value problem involving Riemann Liouville fractional integral boundary conditions on the half line via the Leray-Schauder Nonlinear…

Classical Analysis and ODEs · Mathematics 2021-06-01 Dondu Oz , Ilkay Yaslan Karaca

In order to solve fractional variational problems, there exist two theorems of necessary conditions: an Euler-Lagrange equation which involves Caputo and Riemann-Liouville fractional derivatives, and other Euler-Lagrange equation that…

Optimization and Control · Mathematics 2021-04-12 Melani Barrios , Gabriela Reyero , Mabel Tidball

In this article, we obtain sufficient conditions on existence, uniqueness and Ulam--Hyers stability of solutions for a coupled system of two-point nabla fractional difference boundary value problems, using Banach fixed point theorem and…

General Mathematics · Mathematics 2022-03-09 Jagan Mohan Jonnalagadda

We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problem \label{eq-1} {u^{\prime \prime}}(t)+a(t)f(u(t))=0,\ 0<t<T, u(0)={\beta}u(\eta),\…

Classical Analysis and ODEs · Mathematics 2013-07-05 Faouzi Haddouchi , Slimane Benaicha

We study a nonlocal thermistor problem for fractional derivatives in the conformable sense. Classical Schauder's fixed point theorem is used to derive the existence of a tube solution.

Classical Analysis and ODEs · Mathematics 2018-12-27 Moulay Rchid Sidi Ammi , Delfim F. M. Torres

In this paper, we investigate the existence of solutions for a class of $p$-Laplacian fractional order Kirchhoff-type system with Riemann-Liouville fractional derivatives and a parameter $\lambda$. By mountain pass theorem, we obtain that…

Analysis of PDEs · Mathematics 2019-12-02 Danyang Kang , Cuiling Liu , Xingyong Zhang

In this paper, we study the Dirichlet boundary value problem of steady-state relativistic Boltzmann equation in half-line with hard potential model, given the data for the outgoing particles at the boundary and a relativistic global…

Analysis of PDEs · Mathematics 2024-11-12 Yi Wang , Li Li , Zaihong Jiang

We continue the study of a non self-adjoint fractional three-term Sturm-Liouville boundary value problem (with a potential term) formed by the composition of a left Caputo and left-Riemann-Liouville fractional integral under {\it Dirichlet…

Classical Analysis and ODEs · Mathematics 2022-08-31 Mohammad Dehghan , Angelo B. Mingarelli

Let $\Omega \subset \mathbb R^N$, $N \geq 2$, be a smooth bounded domain. We consider a boundary value problem of the form $$-\Delta u = c_{\lambda}(x) u + \mu(x) |\nabla u|^2 + h(x), \quad u \in H^1_0(\Omega)\cap L^{\infty}(\Omega)$$ where…

Analysis of PDEs · Mathematics 2018-11-02 Colette De Coster , Antonio J. Fernández , Louis Jeanjean

The present paper establishes a certain duality between the Dirichlet and Regularity problems for elliptic operators with $t$-independent complex bounded measurable coefficients ($t$ being the transversal direction to the boundary). To be…

Analysis of PDEs · Mathematics 2014-07-01 Steve Hofmann , Carlos Kenig , Svitlana Mayboroda , Jill Pipher

In a multidimensional infinite layer bounded by two hyperplanes, the Poisson equation with the polynomial right-hand side is considered. It is shown that the Dirichlet boundary value problem and the mixed Dirichlet-Neumann boundary value…

Mathematical Physics · Physics 2017-10-17 Oleg D. Algazin