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A sub-supersolution approach for Neumann boundary value problems with gradient dependence |
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| Affiliation: | 1. Faculty of Education, University of Ljubljana, Kardeljeva ploščad 16, SI-1000 Ljubljana, Slovenia;2. Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia;3. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia;4. Faculty of Computer Science and Informatics, University of Ljubljana, Jadranska 21, SI-1000 Ljubljana, Slovenia;1. Département de Mathématiques, Université de Perpignan, 66860 Perpignan, France;2. Department of Mathematics, Tokyo University of Science, Kagurazaka 1-3, Shinjyuku-ku, Tokyo 162-8601, Japan |
| Abstract: | Existence and location of solutions to a Neumann problem driven by an nonhomogeneous differential operator and with gradient dependence are established developing a non-variational approach based on an adequate method of sub-supersolution. The abstract theorem is applied to prove the existence of finitely many positive solutions or even infinitely many positive solutions for a class of Neumann problems. |
| Keywords: | Quasilinear elliptic equation Neumann problem Gradient dependence Sub-supersolution Positive solution |
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