Two constant sign solutions for a nonhomogeneous Neumann boundary value problem

Liliana Klimczak

doi:10.1515/aupcsm-2015-0004

.blurhash-client-img { display: none !important; }

Two constant sign solutions for a nonhomogeneous Neumann boundary value problem

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 14 (2015): Issue 1 (December 2015)

By: Liliana Klimczak

Open Access

|Dec 2015

Abstract

We consider a nonlinear Neumann problem with a nonhomogeneous elliptic differential operator. With some natural conditions for its structure and some general assumptions on the growth of the reaction term we prove that the problem has two nontrivial solutions of constant sign. In the proof we use variational methods with truncation and minimization techniques.

References

[1] E. Casas, L.A. Fernández, A Green’s formula for quasilinear elliptic operators, J. Math. Anal. Appl., 142 (1989), no. 1, 62-73. Cited on 50.
Search in Google Scholar
[2] L. Damascelli, Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results, Ann. Inst. H. Poincaré. Analyse non linéaire, 15 (1998), no. 4, 493-516. Cited on 47 and 52.
Search in Google Scholar
[3] L. Gasiński, N.S. Papageorgiou, Nonlinear Analysis, Series in Mathematical Analysis and Applications 9, Chapman and Hall/CRC Press, Boca Raton, FL, 2006. Cited on 59.
Search in Google Scholar
[4] G. Leoni, A First Course in Sobolev Spaces, Graduate Studies in Mathematics 105, American Mathematical Society, Providence, RI, 2009. Cited on 60.
Search in Google Scholar
[5] G.M. Lieberman, The natural generalization of the natural conditions of Ladyzhenskaya and Ural’tseva for elliptic equations, Commun. Partial Differential Equations, 16 (1991), no. 1-2, 311-361. Cited on 47 and 48.
Search in Google Scholar
[6] M. Montenegro, Strong maximum principles for supersolutions of quasilinear elliptic equations, Nonlinear Anal., 37 (1999), no. 4, 431-448. Cited on 47.
Search in Google Scholar
[7] D. Motreanu, N.S. Papageorgiou, Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operators, Proc. Amer. Math. Soc., 139 (2011), no. 10, 3527-3535. Cited on 47.
Search in Google Scholar
[8] P. Pucci, J. Serrin, The Maximum Principle, Progress in Nonlinear Differential Equations and their Applications 73, Birkhäuser Verlag, Basel, 2007. Cited on 49.
Search in Google Scholar
[9] E. Zeidler, Nonlinear Functional Analysis and Its Applications II/B. Nonlinear Monotone operators, Springer-Verlag, New York, 1990. Cited on 48, 52 and 57.
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.1515/aupcsm-2015-0004 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

Journal RSS Feed

Language: English

Page range: 47 - 62

Submitted on: Jan 8, 2015

Published on: Dec 30, 2015

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Related subjects:

Mathematics,

General mathematics

© 2015 Liliana Klimczak, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 14 (2015): Issue 1 (December 2015)