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We demonstrate a kind of linear superposition for a large number of nonlinear equations, both continuum and discrete. In particular, we show that whenever a nonlinear equation admits solutions in terms of Jacobi elliptic functions…

Exactly Solvable and Integrable Systems · Physics 2015-06-15 Avinash Khare , Avadh Saxena

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

In this paper, we show existence of \textit{continuums} of positive solutions for non-local quasilinear problems with strongly-singular reaction term on a bounded domain in $\mathbb{R}^N$ with $N \geq 2$. We approached non-autonomous and…

Analysis of PDEs · Mathematics 2018-11-14 Carlos Alberto Santos , Lais Santos , Pawan Kumar Mishra

Classical results of second order parabolic quasi-linear equations always require that the nonlinear terms are controlled by a power of the unknown functions and their first derivatives. We improve the previous results. More precisely, in…

Analysis of PDEs · Mathematics 2022-12-06 Zonglin Jia

In this paper, we study a class of generalized extensible beam equations with a superlinear nonlinearity \begin{equation*} \left\{ \begin{array}{ll} \Delta ^{2}u-M\left( \Vert \nabla u\Vert _{L^{2}}^{2}\right) \Delta u+\lambda V(x) u=f(…

Analysis of PDEs · Mathematics 2018-12-10 Juntao Sun , Tsung-fang Wu

By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…

Classical Analysis and ODEs · Mathematics 2021-02-09 Alberto Cabada , Gennaro Infante , F. Adrián F. Tojo

We extend some classical results dealing with boundary Harnack inequatilities to a class of quasilinear elliptic equations and derive some new estimates for solutions of such equations with an isolated singularity on the boundary of a…

Analysis of PDEs · Mathematics 2007-05-23 Marie-Francoise Bidaut-Veron , Rouba Borghol , Laurent Veron

We show the existence of infinitely many positive solutions, defined on the real line, for the nonlinear scalar ODE \[ \ddot u + (a^+(t) - \mu a^-(t)) u^3 = 0, \] where $a$ is a periodic, sign-changing function, and the parameter $\mu>0$ is…

Classical Analysis and ODEs · Mathematics 2014-07-08 Vivina Barutello , Alberto Boscaggin , Gianmaria Verzini

In this paper, we are concerned with a quasilinear Schrodinger equation with well-known Berestycki--Lions nonliearity. The existence of infinitely many normalized solutions is obtained via a minimax argument.

Analysis of PDEs · Mathematics 2023-05-10 Xianyong Yang , Fukun Zhao

Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit…

solv-int · Physics 2007-05-23 Alexander Turbiner , Pavel Winternitz

In this paper, we consider a generalized strong vector quasi-equilibrium problem and we prove the existence of its solutions by using some suxiliary results. One of the established theorems is proved by using an approximation method.

Optimization and Control · Mathematics 2016-05-11 Monica Patriche

We consider a nonlinear integral equation with infinitely many derivatives that appears when a system of interacting open and closed strings is investigated if the nonlocality in the closed string sector is neglected. We investigate the…

Mathematical Physics · Physics 2008-11-26 L. Joukovskaya

The existence of a formal particular solution (family of solutions) of oscillating type under certain conditions has been proved for the quasi-linear ordinary differential equations system. The asymptotic nature of this solution (the family…

Classical Analysis and ODEs · Mathematics 2013-07-01 Kirill Vadimovich Amelkin , Alexander Vasilevich Kostin

We consider singular quasilinear elliptic systems with homogeneous Dirichlet boundary condition. Using Leray-Schauder topological degree, combined with the sub-supersolutions method and suitable truncation arguments, we establish the…

Analysis of PDEs · Mathematics 2025-10-27 Nouredine Medjoudj , Abdelkrim Moussaoui

In this work we use variational methods to prove results on existence and concentration of solutions to a problem in $\mathbb{R}^N$ involving the $1-$Laplacian operator. A thorough analysis on the energy functional defined in the space of…

Analysis of PDEs · Mathematics 2017-02-23 C. O. Alves , M. T. O. Pimenta

In this paper, we investigate the existence of nontrivial weak solutions to a class of elliptic equations ($\mathscr{P}$) involving a general nonlocal integrodifferential operator $\mathscr{L}_{\mathcal{A}K}$, two real parameters, and two…

Analysis of PDEs · Mathematics 2020-03-31 Lauren Maria Mezzomo Bonaldo , Olmpio Hiroshi Miyagaki , Elard Jurez Hurtado

This paper is devoted to the following class of nonlinear fractional Schr\"odinger equations: \begin{equation*} (-\Delta)^{s} u + V(x)u = f(x,u) + \lambda g(x,u), \quad \text{in}\: \mathbb{R}^N, \end{equation*} where $s\in (0,1)$, $N>2s$,…

Analysis of PDEs · Mathematics 2023-01-10 Sofiane Khoutir

In this article using Nehari manifold method we study the multiplicity of solutions of the following nonlocal elliptic system involving variable exponents and concave-convex nonlinearities: \begin{equation*} \;\;\; \begin{array}{rl}…

Analysis of PDEs · Mathematics 2020-04-21 Reshmi Biswas , Sweta Tiwari

Solutions which are quasimodular forms to a second order differential equation attached to a triangular group are explicitly described in terms of certain orthogonal polynomials.

Number Theory · Mathematics 2007-05-23 Masanobu Kaneko , Masao Koike

We prove that a class of superlinear indefinite problems with homogeneous Neumann boundary conditions admits an arbitrarily high number of positive solutions, provided that the parameters of the problem are adequately chosen. The…

Classical Analysis and ODEs · Mathematics 2018-07-19 Andrea Tellini