We consider the existence of bound states for the coupled elliptic system ∆u 1 − λ 1 u 1 + µ 1 u 3
Recommended by Thomas Bartsch We give some new definitions of D *-metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly commuting mappings in complete D *-metric spaces. We get some improved versions of several fixed point theorems in complete D *-metric spaces.
We consider the Hamiltonian system (HS) ?J _ z = H z (t; z) where H 2 C 2 (R R 2N ; R) is 2-periodic in all variables, so (HS) induces a Hamiltonian system on the torus T 2N. In addition we assume that H is even in the z-variable. This implies the existence of 2 2N trivial stationary solutions of (HS). We are interested in the existence of nontrivial… (More)
The paper is concerned with the local and global bifurcation structure of positive solutions u, v ∈ H 1 0 (() of the system −u + u = µ 1 u 3 + βv 2 u in −v + v = µ 2 v 3 + βu 2 v in of nonlinear Schrödinger (or Gross-Pitaevskii) type equations in ⊂ R N , N ≤ 3. The system arises in nonlinear optics and in the Hartree–Fock theory for a double condensate.… (More)
This paper introduces a framework for a highly constrained sports scheduling problem which is modeled from the requirements of various professional sports leagues. We define a sports scheduling problem, introduce the necessary terminology and detail the constraints of the problem. A set of artificial and real-world instances derived from the actual problems… (More)
Recent developments in transition state theory brought about by dynamical systems theory are extended to time-dependent systems such as laser-driven reactions. Using time-dependent normal form theory, the authors construct a reaction coordinate with regular dynamics inside the transition region. The conservation of the associated action enables one to… (More)
Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation f2x y 4fx fy fx y − fx − y in Banach spaces.
The crossing of a transition state in a multidimensional reactive system is mediated by invariant geometric objects in phase space: An invariant hyper-sphere that represents the transition state itself and invariant hyper-cylinders that channel the system towards and away from the transition state. The existence of these structures can only be guaranteed if… (More)