A note on the topological degree at a critical point of mountainpass-type
A note on the topological degree at a critical point of mountainpass-type
In this note we will show that the local degree at an isolated critical point given by the Ambrosetti-Rabinowitz mountainpass-theorem is <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="negative 1"> <mml:semantics> <mml:mrow> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">- 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for a large class of functionals. This class includes for …