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In this paper, we study the global existence and nonexistence of positive solutions to the following nonlinear reaction-di usion system 8>>>>>>>>>>>>< >>>>>>>>>>>>: ut 􀀀 u = W(x)vp + S(x...
The author shows the interpolation inequalities for derivatives in variable exponent Lebesgue-Sobolev spaces by applying the boundedness of the Hardy-Littlewood maximal operator on L^{p(x)}. As applic...
We study a functional with variable exponent, 1 Keywords: variational exponent functional;BV space;staircasing effect;heat
Abstract The function space L^{p(x)}(Omega) with unbounded variable exponent, which generalizing the space L^{p(x)}(Omega) with bounded variable exponent, is investigated in this paper. We have define...
Abstract: This paper continues a study on trajectories of Brownian Motion in a field of soft trap whose radius distribution is unbounded. We show here for both point-to-point and point-to-plane model ...
Abstract: We consider the design and analysis of numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exponents. Th...
The heat-bal ance in te gral method of Good man has been thor oughly an a lyzed in the case of a par a bolic pro file with un spec i fied ex po nent de pend ing on the bound ary con di tion im posed. ...
The heat-bal ance in te gral method of Good man is stud ied with two sim ple 1-D heat con duc tion prob lems with pre scribed tem per a ture and flux bound ary con di tions.These clas si cal prob lems...
We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood.We provide conditions under which the pertur...
We study the effect of a random perturbation on a one-parameter family of dynamical systems whose behavior in the absence of perturbation is ill understood.We provide conditions under which the pertur...
Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $\exp(G)$ and let $m=\lfloor\log_pk\rfloor$. We show that $\exp(M^{(c)}(G))$ divides $\exp(G)p^{m(k-1)}$, for all $c\geq1$, where $...
We continue our study of the parabolic Anderson equation $\partial u/\partial t = \kappa\Delta u + \gamma\xi u$ for the space-time field $u\colon\,\Z^d\times [0,\infty)\to\R$, where $\kappa \in [0,\in...
A result of the author shows that the behavior of Gowers norms on bounded exponent abelian groups is connected to finite nilspaces. Motivated by this, we investigate the structure of finite nilspaces...
We investigate existence and qualitative behaviour of solutions to nonlinear Schr¨odinger equations with critical exponent and singular electromagnetic potentials. We are concerned with with magnetic ...

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