A method of exponential dichotomy and a Mel'nikov function is used to generalize the results concerning the existence of ground states with fast decay and the existence of singular ground states with slow decay for the scalar curvature equation. The equation has a critical exponent. A constant is given as a bounded function which is radially symmetric, is positive at some point, and has further properties of a simple nature.
On positive solutions of the scalar curvature equation when the curvature has variable sign / R. Johnson; F. Battelli. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 47:(2001), pp. 1029-1037. [10.1016/S0362-546X(01)00243-7]
On positive solutions of the scalar curvature equation when the curvature has variable sign
JOHNSON, RUSSELL ALLAN;
2001
Abstract
A method of exponential dichotomy and a Mel'nikov function is used to generalize the results concerning the existence of ground states with fast decay and the existence of singular ground states with slow decay for the scalar curvature equation. The equation has a critical exponent. A constant is given as a bounded function which is radially symmetric, is positive at some point, and has further properties of a simple nature.
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