MR3114823
Leszek GASIŃSKI and Nikolaos S. PAPAGEORGIOU
Leszek GASIŃSKI and Nikolaos S. PAPAGEORGIOU
Nonlinear Neumann Problems with Constraints
Funkcialaj Ekvacioj. Serio Internacia
56
2013
249--270
http://fe.math.kobe-u.ac.jp/FE/FullPapers/56-2/56_249.pdf
http://www.ams.org/mathscinet-getitem?mr=MR3114823
We consider a $C^1$-functional $\psi$ defined on the ``Neumann'' Sobolev space $W^{1,p}_n(\Omega)$. If $M$ is a $C^1$-submanifold, then for $\psi|_M$ we show that any local $C^1_n(\overline{\Omega})$-minimizer is also a local $W^{1,p}_n(\Omega)$-minimizer. Then we use this general result on local minimizers to show that a nonlinear parametric Neumann problem driven by the $p$-Laplace differential operator and restricted on a sphere, has at least three distinct smooth solutions.
$W^{1,p}$ and $C^1$ local minimizers, $C^1$-manifold, Lagrange multiplier, Duality map, Positive solutions, $p$-Laplacian.
35J25, 35J92.
56-249
2013
Nonlinear Neumann Problems with Constraints
Leszek GASIŃSKI and Nikolaos S. PAPAGEORGIOU
Leszek GASIŃSKI and Nikolaos S. PAPAGEORGIOU
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