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GROUND STATE AND NON-GROUND STATE SOLUTIONS OF SOME STRONGLY COUPLED ELLIPTIC SYSTEMS

Authors
Journal
Transactions of the American Mathematical Society
0002-9947
Publisher
American Mathematical Society
Publication Date
Keywords
  • Elliptic System
  • Ground State Solution
  • Positive Solution
  • Sign Changing Solution
  • Symmetry

Abstract

We study an elliptic system of the form Lu = vertical bar v vertical bar(p-1) v and Lv = vertical bar u vertical bar(q-1) u in Omega with homogeneous Dirichlet boundary condition, where Lu := -Delta u in the case of a bounded domain and Lu := -Delta u + u in the cases of an exterior domain or the whole space R-N. We analyze the existence, uniqueness, sign and radial symmetry of ground state solutions and also look for sign changing solutions of the system. More general non-linearities are also considered.

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