Spurious solutions of three-dimensional Faddeev equations

We obtain explicit spurious solutions of three-dimensional Faddeev equations written in the total angular momentum and total space parity representation. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 227–242, August, 2006.     

Limiting laws for long Brownian bridges perturbed by their one-sided maximum, III

Summary Results of penalization of a one-dimensional Brownian motion ]]>]]>]]>]]>]]>]]>]]>(X_t) $, by its one-sided maximum $\big(S_t=\sup_{0 \leq u \leq t}X_u\big)$, which were recently obtained by the authors are improved with the consideration - in the present paper - of the asymptotic behaviour of the likewise penalized Brownian bridges of length $t$, as $t\rightarrow \infty$, or penalizations by functions of $(S_t,X_t)$, and also the study of the speed of convergence, as $t\rightarrow \infty$, of the penalized distributions at time $t$.     

ON THE EXISTENCE OF POSITIVE ENTIRE SOLUTIONS FOR SINGULAR p-LAPLACE EQUATIONS

In this paper N-dimensional singular, p-Laplace equations of the following form are considered, where p ≥N, β > 0, and f : [0,∞)×(0,∞)×[0, ∞)→[0,∞) is a continuous function. Some sufficient conditions are obtained for the existence of infinitely many radially positive entire solutions of the equation which are asymptotic to positive constant multiples of |x|(p-N)/(p-1) for p > N or log|x| for N = p as |x|→∞.     

Coexistence states for systems of mutualist species

Coexistence states for a class of systems of mutualist species are obtained via bifurcation theory and monotone techniques.     

A nonlinear superposition principle and multibump solutions of periodic Schrödinger equations

In an abstract setting we prove a nonlinear superposition principle for zeros of equivariant vector fields that are asymptotically additive in a well-defined sense. This result is used to obtain multibump solutions for two basic types of periodic stationary Schrödinger equations with superlinear nonlinearity. The nonlinear term may be of convolution type. If the superquadratic term in the energy functional is convex, our results also apply in certain cases if 0 is in a gap of the spectrum of the Schrödinger operator.     

Optimal rigid body motions,part 2: Minimum time solutions

The time-optimal control of rigid-body angular rates is investigated in the absence of direct control over one of the angular velocity components. The existence of singular subarcs in the time-optimal trajectories is explored. A numerical survey of the optimality conditions reveals that, over a large range of boundary conditions, there are in general several distinct extremal solutions. A classification of extremal solutions is presented, and domains of existence of the extremal subfamilies are established in a reduced parameter space. A locus of Darboux points is obtained, and global optimality of the extremal solutions is observed in relation to the Darboux points. The continuous dependence of the optimal trajectories with respect to variations in control constraints is noted, and a procedure to obtain the time-optimal bang-bang solutions is presented.This work was supported in part by DARPA under Contract No. ACMP-F49620-87-C-0016, by SDIO/IST under Contract No. F49620-87-C0088, and by Air Force Grant AFOSR-89-0001.     

ON SOLUTIONS TO SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper, using the theory of resolvent operators, Banach,s contraction prin-ciple and Schauder,s fixed point theorem, we study the existence of integral solutions to semilinear integrodifferential equations under nonlocal conditions in Banach space. An example is provided to illustrate the results obtained.     

Simple Singularities for Hamilton-Jacobi Equations with Max-Concave Hamiltonians and Generalized Characteristics

We consider piecewise smooth viscosity solutions to a Hamilton-Jacobi equation, for which the Hamiltonian is the maximum of a finite number of smooth concave functions. We describe the possible types of “basic” singularities, namely jump discontinuities in either the derivative of the solution or the Hamiltonian, which occur across a smooth hypersurface. Each such type of singularity is described in terms of the properties of the Hamiltonian and the classical characteristics in the regions on either side of the singularity. Where appropriate, singular characteristic equations of the types developed by Melikyan are formulated which can be used in constructions.     

Global existence of strong solutions to the Cauchy problem for a 1D radiative gas

We consider a one-dimensional radiation hydrodynamics model in the case of the equilibrium diffusion approximation which is described by the compressible Navier-Stokes system with the additional terms in the pressure and internal energy respectively, which embody the effect of radiation. Under the physical growth conditions on the heat conductivity, we establish the existence and uniqueness of strong solutions to the Cauchy problem with large initial data, where the initial density and velocity may have differing constant states at infinity. Moreover, we show that if there is no vacuum in the initial density, then, the vacuum and concentration of the density will never occur in any finite time.