Two constant sign solutions for a nonhomogeneous Neumann boundary value problem
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
E. Casas, L.A. Fernández, A Green’s formula for quasilinear elliptic operators, J. Math. Anal. Appl., 142 (1989), no. 1, 62–73.
##plugins.generic.googleScholarLinks.settings.viewInGS##
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.
##plugins.generic.googleScholarLinks.settings.viewInGS##
L. Gasiński, N.S. Papageorgiou, Nonlinear Analysis, Series in Mathematical Analysis and Applications 9, Chapman and Hall/CRC Press, Boca Raton, FL, 2006.
##plugins.generic.googleScholarLinks.settings.viewInGS##
G. Leoni, A First Course in Sobolev Spaces, Graduate Studies in Mathematics 105, American Mathematical Society, Providence, RI, 2009.
##plugins.generic.googleScholarLinks.settings.viewInGS##
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.
##plugins.generic.googleScholarLinks.settings.viewInGS##
M. Montenegro, Strong maximum principles for supersolutions of quasilinear elliptic equations, Nonlinear Anal., 37 (1999), no. 4, 431–448.
##plugins.generic.googleScholarLinks.settings.viewInGS##
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.
##plugins.generic.googleScholarLinks.settings.viewInGS##
Liliana Klimczak
##plugins.generic.googleScholarLinks.settings.viewInGS##
P. Pucci, J. Serrin, The Maximum Principle, Progress in Nonlinear Differential Equations and their Applications 73, Birkhäuser Verlag, Basel, 2007.
##plugins.generic.googleScholarLinks.settings.viewInGS##
E. Zeidler, Nonlinear Functional Analysis and Its Applications II/B. Nonlinear Monotone operators, Springer-Verlag, New York, 1990. Cited on 48, 52 and 57. Faculty of Mathematics and Computer Science Jagiellonian University Lojasiewicza 6 30-048 Krakow Poland E-mail: liliana.klimczak@uj.edu.pl Received: January 8, 2015; final version: March 16, 2015; available online: April 28, 2015.
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