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Given a spatially dependent mass we obtain the two-point Green's function for exactly solvable nonrelativistic problems. This is accomplished by mapping the wave equation for these systems into well-known exactly solvable Schrodinger…

Condensed Matter · Physics 2016-08-31 A. D. Alhaidari

In this paper, we establish some common fixed point results for two pairs of weakly compatible mappings in the setting of $C$-complex valued metric space. Also, as application of the proved result, we obtain the existence and uniqueness of…

Functional Analysis · Mathematics 2017-09-12 Deepak Kumar , Sumit Chandok

This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new…

Analysis of PDEs · Mathematics 2008-05-01 Michael Robinson

A simple and general approach for calculating the elliptic finite-gap solutions of the Korteweg-de Vries (KdV) equation is proposed. Our approach is based on the use of the finite-gap equations and the general representation of these…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 Andrii Korostil

In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].

Functional Analysis · Mathematics 2025-04-22 Yacine Chitour , Jochen Denzler , Frédéric Jean , Emmanuel Trélat

The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and…

General Relativity and Quantum Cosmology · Physics 2010-12-13 Kei Yamada , Hideki Asada

The aim of this paper is to study global bifurcations of non-constant solutions of some nonlinear elliptic systems, namely the system on a sphere and the Neumann problem on a ball. We study the bifurcation phenomenon from families of…

Analysis of PDEs · Mathematics 2021-07-02 Anna Gołębiewska , Joanna Kluczenko , Piotr Stefaniak

An approach is proposed to obtain some exact explicit solutions in terms of the Weierstrass' elliptic function $\wp$ to a generalized Benjamin-Bona-Mahony (BBM) equation. Conditions for periodic and solitary wave like solutions can be…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 J. Nickel

We consider the bifurcation diagram of radial solutions for the Gelfand problem with a positive radially symmetric weight in the unit ball. We deal with the exponential nonlinearity and a power-type nonlinearity. When the weight is…

Analysis of PDEs · Mathematics 2024-09-04 Kenta Kumagai

In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…

Instrumentation and Methods for Astrophysics · Physics 2015-05-13 András Pál

We study a two-point boundary value problem for a linear differen\-tial-algebraic equation with constant coefficients by using the method of parameterization. The parameter is set as the value of the continuously differentiable component of…

Classical Analysis and ODEs · Mathematics 2023-07-07 Anar Assanova , Carsten Trunk , Roza Uteshova

We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…

Numerical Analysis · Mathematics 2020-03-31 S. Armstrong , A. Hannukainen , T. Kuusi , J. -C. Mourrat

We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a…

Mathematical Physics · Physics 2009-12-10 A. S. Fokas , B. Pelloni

In the present work, we establish the existence and multiplicity of positive solutions for the singular elliptic equations with a double weighted nonlocal interaction term defined in the whole space $\mathbb{R}^N$. The nonlocal term and the…

Analysis of PDEs · Mathematics 2025-03-11 Márcia S. B. A. Cardoso , Edcarlos D. Silva , Marcos. L. M. Carvalho , Minbo Yang

In this paper, after reviewing the form of the constitutive equations for a third grade Korteweg fluid, recently derived by means of an extended Liu procedure, an equilibrium problem is investigated. By considering a two--dimensional…

Mathematical Physics · Physics 2025-05-29 M. Gorgone , F. Oliveri , A. Ricciardello , P. Rogolino

We consider the Gelfand problem with rapidly growing nonlinearities in the two-dimensional bounded strictly convex domains. In this paper, we prove the uniformly boundedness of finite Morse index solutions. As a result, we show that there…

Analysis of PDEs · Mathematics 2025-06-17 Kenta Kumagai

In this paper, we prove existence and regularity of positive solutions for singular quasilinear elliptic systems involving gradient terms. Our approach is based on comparison properties, a priori estimates and Schauder's fixed point…

Analysis of PDEs · Mathematics 2021-03-16 Halima Dellouche , Abdelkrim Moussaoui

In this paper, we construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation. This procedure is carried out by constructing solutions to the following elliptic…

Analysis of PDEs · Mathematics 2015-06-11 Daomin Cao , Zhongyuan Liu , Juncheng Wei

The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more…

Earth and Planetary Astrophysics · Physics 2015-08-11 Z. E. Musielak , B. Quarles

In this paper, we deal with a class of semilinear elliptic equation in a bounded domain $\Omega\subset\mathbb{R}^N$, $N\geq 3$, with $C\sp{1,1}$ boundary. Using a new fixed point result of the Krasnoselskii's type for the sum of two…

Analysis of PDEs · Mathematics 2007-05-23 Cleon S. Barroso