Results 61 to 70 of about 671 (73)

On Struwe-Jeanjean-Toland monotonicity trick [PDF]

arXiv, 2010
The abstract version of Struwe's monotonicity trick developed by Jeanjean and Jeanjean-Toland for functionals depending on a real parameter is improved, under suitable assumptions. Besides, all the machinery is extended to the case of continuous functionals on Banach spaces, in the framework of non-smooth critical point theory.
arxiv  

Solutions of elliptic equations with a level surface parallel to the boundary: stability of the radial configuration

, 2013
Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of their level surfaces is parallel to ...
Ciraolo, Giulio, Magnanini, Rolando, Sakaguchi, Shigeru   +2 more
core  

On variational bivectors [PDF]

arXiv
We construct examples of variational bivectors that are not Poissonian.
arxiv  

On a bifurcation value related to quasi-linear Schrodinger equations [PDF]

arXiv, 2011
By virtue of numerical arguments we study a bifurcation phenomenon occurring for a class of minimization problems associated with the quasi-linear Schrodinger equation.
arxiv  

Radial Symmetry of Large Solutions of Semilinear Elliptic Equations with Convection [PDF]

arXiv, 2012
We study radial symmetry of large solutions of the semi-linear elliptic problem \Delta u + \nabla h.\nabla u = f(|x|,u), and we provide sharp conditions under which the problem has a radial solution. The result is independent of the rate of growth of the solution at infinity.
arxiv  

Symmetry of n-mode positive solutions for two-dimensional Hénon type systems [PDF]

arXiv, 2013
We provide a symmetry result for n-mode positive solutions of a general class of semi-linear elliptic systems under cooperative conditions on the nonlinearities. Moreover, we apply the result to a class of H\'enon systems and provide the existence of multiple n-mode positive solutions.
arxiv  

Asymptotics of ground states for fractional Hénon systems [PDF]

arXiv, 2014
We investigate the asymptotic behavior of positive ground states for H\'enon type systems involving a fractional Laplacian on a bounded domain, when the powers of the nonlinearity approach the Sobolev critical exponent.
arxiv  

Exact Solutions of a Mathematical Model Describing Competition and Co-Existence of Different Language Speakers. [PDF]

Entropy (Basel), 2020
Cherniha R, Davydovych V.
europepmc   +1 more source

Uniform Lipschitz regularity of flat segregated interfaces in a singularly perturbed problem [PDF]

arXiv, 2015
For the singularly perturbed system \[\Delta u_{i,\beta}=\beta u_{i,\beta}\sum_{j\neq i}u_{j,\beta}^2, \quad 1\leq i\leq N,\] we prove that flat interfaces are uniformly Lipschitz. As a byproduct of the proof we also obtain the optimal lower bound near the flat interfaces, \[\sum_iu_{i,\beta}\geq c\beta^{-1/4}.\]
arxiv  

Symmetrization and anti-symmetrization in parabolic equations [PDF]

arXiv, 2016
We derive some symmetrization and anti-symmetrization properties of parabolic equations. First, we deduce from a result by Jones a quantitative estimate of how far the level sets of solutions are from being spherical. Next, using this property, we derive a criterion providing solutions whose level sets do not converge to spheres for a class of ...
arxiv