caa a22 4500 44584373X CHVBK 20180317145352.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00526-011-0390-2 doi (NATIONALLICENCE)springer-10.1007/s00526-011-0390-2 Anisotropic nonlinear Neumann problems [Elektronische Daten] [Leszek Gasiński, Nikolaos Papageorgiou] We consider nonlinear Neumann problems driven by the p(z)-Laplacian differential operator and with a p-superlinear reaction which does not satisfy the usual in such cases Ambrosetti-Rabinowitz condition. Combining variational methods with Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive, the other negative). In the process, we also prove two results of independent interest. The first is about the L ∞-boundedness of the weak solutions. The second relates W 1,p(z) and C 1 local minimizers. The Author(s), 2011 Gasiński Leszek Institute of Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348, Kraków, Poland aut Papageorgiou Nikolaos Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece aut Calculus of Variations and Partial Differential Equations Springer-Verlag 42/3-4(2011-11-01), 323-354 0944-2669 42:3-4<323 2011 42 526 https://doi.org/10.1007/s00526-011-0390-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-011-0390-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gasiński Leszek Institute of Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348, Kraków, Poland aut NATIONALLICENCE 700 1- Papageorgiou Nikolaos Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 42/3-4(2011-11-01), 323-354 0944-2669 42:3-4<323 2011 42 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer