using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of monge-amp`{e}re equations are established‎.‎

A classic problem, the design of the tallest column, is solved again using a different method. By the use of a similarity solution the equations are transformed and the difficult singularity at the endpoint is peeled away. The resulting autonomous system has a critical point and the solution must be on its stable manifold. The solution is found by starting near the critical point in the directi...

today, along with enhancement of social well-being andeconomic development, demand for transportation is growing increasingly.many countries are seeking for providing transportation servicesat a reasonable price. therefore, optimization of carrying goods on nationalor international roads is highly important in terms of costs andtransportation indicator, so that the goods are shipped at minimumc...

We construct an order reconstruction (OR)-type Landau-de Gennes critical point on a square domain of edge length 2λ, motivated by the well order reconstruction solution numerically reported in [1]. The OR critical point is distinguished by an uniaxial cross with negative scalar order parameter along the square diagonals. The OR critical point is defined in terms of a saddle-type critical point ...

Problem (1.1) appears in applied mathematics. See for example [13, 14] and the references therein. For the interesting link between this problem and the modelling of activator-inhibitor systems, the authors can refer to [11]. In [13, 14], Ni and Takagi prove that the least energy solution of (1.1) has exactly one local maximum point xε which lies in ∂Ω, and xε tends to a point x0 which attains ...

We consider the mass-critical focusing nonlinear Schrödinger equation in the presence of an external potential, when the nonlinearity is inhomogeneous. We show that if the inhomogeneous factor in front of the nonlinearity is sufficiently flat at a critical point, then there exists a solution which blows up in finite time with the maximal (unstable) rate at this point. In the case where the crit...

We consider the mass-critical focusing nonlinear Schrödinger equation in the presence of an external potential, when the nonlinearity is inhomogeneous. We show that if the inhomogeneous factor in front of the nonlinearity is sufficiently flat at a critical point, then there exists a solution which blows up in finite time with the maximal (unstable) rate at this point. In the case where the crit...

We consider the mass-critical focusing nonlinear Schrödinger equation in the presence of an external potential, when the nonlinearity is inhomogeneous. We show that if the inhomogeneous factor in front of the nonlinearity is sufficiently flat at a critical point, then there exists a solution which blows up in finite time with the maximal (unstable) rate at this point. In the case where the crit...

The notion of the necessary criticality (both with respect to path and to activity) of a network with imprecisely defined (by means of intervals or fuzzy intervals) activity duration times is introduced and analyzed. It is shown, in the interval case, that both the problem of asserting whether a given path is necessarily critical and the problem of determining an arbitrary necessarily critical ...