A counterexample to the Fredholm alternative for the ๐-Laplacian
A counterexample to the Fredholm alternative for the ๐-Laplacian
The following nonhomogeneous Dirichlet boundary value problem for the one-dimensional <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Laplacian with <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="1 greater-than p greater-than normal infinity"> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>></mml:mo> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mi mathvariant="normal">โ</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">1 > p > \infty</mml:annotation> </mml:semantics> </mml:math> โฆ