Related papers: Non-trivial solution to a simple problem
We prove the existence of a non-trivial solution for a nonlinear equation related to a measure-valued Lagrangian. The result is based on a compact embedding theorem of the Lagrangian domain and on the application of the Mountain Pass…
Leaves and flowers frequently have a characteristic rippling pattern at their edges. Recent experiments found similar patterns in torn plastic. These patterns can be reproduced by imposing metrics upon thin sheets. The goal of this paper is…
This paper is dedicated to the unique continuation properties of the solutions to nonlinear variational problems. Our analysis covers the case of nonlinear autonomous functionals depending on the gradient, as well as more general double…
This article is concerned with the mathematical analysis of a class of a nonlinear fractional Schrodinger equations with a general Hartree-type integrand. We prove existence and uniqueness of global-in-time solutions to the associated…
We study a chain of anharmonic springs with tunable power law interactions as a minimal model to explore the propagation of strongly non-linear solitary wave excitations in a background of thermal fluctuations. By treating the solitary…
In this paper, we determine the transverse instability of periodic standing wave solutions for the generalized Schr\"odinger equation with fractional power nonlinearity. The existence of periodic waves is determined by using a constrained…
Starch solutions, which are strongly non-Newtonian, show a surface instability, when subjected to a load. A droplet of the fluid is sandwiched between two glass plates and a weight varying from 1 to 5 kgs. is placed on the top plate. The…
In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity $\Omega$, such that it has positive vorticity and is concentrated in a finite disjoint union…
We explore physics of unstable particles when mother particle mass is around the sum of its daughter particle masses. In this case, the conventional wave function renormalization factor is ill-defined. We propose a simple resolution of the…
We derive scaling laws for the steady spectrum of wind excited waves, assuming two inviscid fluids (air and water) and no surface tension, an approximation valid at large speeds. In this limit there exists an unique (small) dimensionless…
We study the spectrum of non-homogeneous partially hinged plates having structural engineering applications. A possible way to prevent instability phenomena is to maximize the ratio between the frequencies of certain oscillating modes with…
We consider {\it small solutions} of a vibrating mechanical system with smooth non-linearities for which we provide an approximate solution by using a triple scale analysis; a rigorous proof of convergence of the triple scale method is…
The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one-phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions $n\geq3$ is completely open. In…
In this work, we study the in-plane oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Melnikov-type analysis is applied for the persistence of periodic oscillations of a reduced…
We consider non-stationary localized oscillations of an infinite Bernoulli-Euler beam. The beam lies on the Winkler foundation with a point inhomogeneity (a concentrated spring with negative time-varying stiffness). In such a system with…
In this paper the statement of the second Bogolyubov's theorem on periodic solutions of smooth systems with small parameter is justified for discountinuous systems. It is assumed that the generating solution intersects the discontinuity…
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…
The aim of our work is to provide a simple homogenization and discrete-to-continuum procedure for energy driven problems involving stochastic rapidly-oscillating coefficients. Our intention is to extend the periodic unfolding method to the…
We determine the smallest instantaneous increase in the strength of an opposing wind that is necessary to permanently reverse the forward displacement flow that is driven by a two-layer thermal stratification. With an interpretation in…
There is growing interest in molecular structures that exhibit dynamics similar to bistable mechanical systems. These structures have the potential to be used as nanodevices with two distinct states. Particularly intriguing are structures…