A Mixed Case

  • Paul H. Rabinowitz
  • Edward W. Stredulinsky
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 81)


Two rather different types of multitransition solutions were studied in Chaps. 6–10: those lying between a given gap pair v0 < w0 and those that have the monotonicity property.\(u < \tau^1_{\_1} u\) and cross gaps. The goal of this section is to combine these two cases. Thus we seek solutions of (PDE) that are heteroclinics or homoclinics as a function of x1, lie in prescribed gaps for x1 near \(\pm \infty\),and undergo a prescribed number of transitions between a given set of gap pairs. Roughly speaking, such solutions can be obtained by concatenating those of Chapters 6–10. Different kinds of results are possible depending on how precisely one seeks to shadow the states that are glued together.


Maximum Principle Lipschitz Constant Obstacle Problem Admissible Function Constraint Region 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA
  2. 2.Department of MathematicsUniversity of Wisconsin-Rock CountyJanesvilleUSA

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