MR3099034 Michael E. FILIPPAKIS and Nikolaos S. PAPAGEORGIOU Michael E. FILIPPAKIS and Nikolaos S. PAPAGEORGIOU Nodal Solutions for Neumann Problems with a Nonhomogeneous Differential Operator Funkcialaj Ekvacioj. Serio Internacia 56 2013 63--79 http://fe.math.kobe-u.ac.jp/FE/FullPapers/56-1/56_63.pdf http://www.ams.org/mathscinet-getitem?mr=MR3099034 We consider a nonlinear elliptic Neumann problem driven by a nonhomogeneous differential operator, which is strictly monotone and incorporates as special cases the $p$-Laplacian, the $(p,q)$-differential operator and the generalized $p$-mean curvature differential operator. Using variational methods coupled with suitable truncation and comparison techniques and Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions, one positive, the second negative and the third nodal. Also we show that the problem has extremal nontrivial constant sign solutions. Nonhomogeneous differential operator, Nonlinear regularity, Nonlinear strong maximum principle, Extremal constant sign solutions, Nodal solution, Local minimizer. 35J20, 35J60. 56-63 2013 Nodal Solutions for Neumann Problems with a Nonhomogeneous Differential Operator Michael E. FILIPPAKIS and Nikolaos S. PAPAGEORGIOU Michael E. FILIPPAKIS and Nikolaos S. PAPAGEORGIOU 1 Aizicovici, S.; Papageorgiou, N. S.; Staicu, V. Degree theory for operators of monotone type and nonlinear elliptic equations with inequality constraints Mem. Amer. Math. Soc. 196, no. 915 2008 MR2459421
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