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We consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric...
Let p be a prime, P a finite p-group and F a Frobenius P-category. The question on the existence of a suitable category L^sc extending the full subcategory of F over the set of F-selfcentralizing subg...
Abstract: We prove that any unitary representation of GL(n;R) and GL(n;C) admits an equivariant linear form with respect to one of the subgroups considered by Klyachko.
Some superlinear fourth order elliptic equations are considered. Ground states are proved to exist and to concentrate at a point in the limit. The proof relies on variational methods, where the existe...
In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical resu...
We present some numerical findings concerning the nature of the blowup vs. global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation in three dimensions for radial data. The co...
This work deals with the system $(-\Delta)^m u= a(x)\, v^p$, $(-\Delta)^m v=b(x)\, u^q$ with Dirichlet boundary condition in a domain $\Omega\subset\RR^n$, where $\Omega$ is a ball if $n\ge 3$ or a sm...
In this paper, we consider the global existence and blowup phenomena of the following Cauchy problem−iut = u − V (x)u + f(x, |u|2)u + (W ⋆ |u|2)u, x ∈ RN, t > 0,u(x, 0) = u0(x), x ...
In this paper, we prove the existence of classical solutions of the Dirichlet problem for a class of quasi-linear elliptic equations on unbounded domains like a cone or a U-type domain in Rn(n ≥ 2). T...
In this work we investigate solvable and nilpotent Lie groups with special metrics. The metrics of interest are left-invariant Einstein and algebraic Ricci soliton metrics. Our main result shows that ...
4) is the critical sobolev exponent. This result is a extension of [1].
In this paper, we consider a system of two cubic quasi-linear Klein--Gordon equations with different masses for small, smooth, compactly supported Cauchy data in one space dimension. We show that such...
In this paper, we generalize the fixed point theorem of cone expansion and compression of norm type to the theorem of functional type. As an application, the existence of positive solutions for some f...
Using the technique of annihilators, we characterize the $w^{*}$-closure of the finite-partition submodule ${{\mathscr R}({\mathscr N}, \sim)}$ of a weakly closed nest algebra module ${\mathscr U}$ co...
This paper deals with the strongly coupled parabolic system $u_{t}=v^{m}{\Delta}u,v_{t}=u^{n}{\Delta}v,\ (x,t)$ $\in {\Omega}\times (0,T)$ subject to nonlinear boundary conditions ${\partial}u/{\parti...

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