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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)
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)
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)
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)
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)