Nonlinear Neumann problems with indefinite potential and concave terms

Communications on Pure and Applied Analysis - Tập 14 Số 6 - Trang 2561-2616 - 2015
Shouchuan Hu, Nikolaos S. Papageorgiou

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S. Aizicovici, 2008, <em>Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints</em>,, Memoirs, 10.1090/memo/0915

H. Amann, 1979, Saddle points and multiple solutions of differential equations,, \emph{Math. Z.}, 169, 127, 10.1007/BF01215273

A. Ambrosetti, 1994, Combined effects of concave and convex nonlinearities in some elliptic problems,, \emph{J. Functional Anal.}, 122, 519, 10.1006/jfan.1994.1078

G. Barletta, 2014, A nonlinear eigenvalue problem for the periodic scalar $p$-Laplacian,, \emph{Comm. Pure. Appl. Anal.}, 13, 1075, 10.3934/cpaa.2014.13.1075

A. Castro, 1979, Critical point theory and the number of solutions of a nonlinear Dirichlet problem,, \emph{Ann. Mat. Pura Appl.}, 120, 113, 10.1007/BF02411940

A. Castro, 2013, Existence and qualitative properties of solutions for nonlinear Dirichlet problems,, \emph{Discrete Cont Dyn Systems}, 33, 123, 10.3934/dcds.2013.33.123

L. Cherfils, 2005, On the stationary solutions of generalized reaction diffusion equations with p&q Laplacian,, \emph{Commun. Pure Appl. Anal.}, 4, 9, 10.3934/cpaa.2005.4.9

G. M. Coclite, 2013, On a Dirichlet problem in bounded domains with singular nonlinearity,, \emph{Discrete Contin. Dynam. Systems}, 33, 4923, 10.3934/dcds.2013.33.4923

Y. Deng, 2012, Existence of multiple solutions for a nonhomogeneous semilinear elliptic equatio involving critical exponent,, \emph{Discrete Contin. Dynam. Systems}, 32, 795, 10.3934/dcds.2012.32.795

M. Filippakis, 2013, Nodal solutions for Neumann problems with a nonhomogeneous differential operator,, \emph{Funkc. Ekv.}, 56, 63, 10.1619/fesi.56.63

M. Filippakis, 2009, Existence of five nonzero solutions with exact sign for a $p$-Laplacian equation,, \emph{Discrete Cont Dyn Systems}, 24, 405, 10.3934/dcds.2009.24.405

J. Garcia Azorero, 2000, Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations,, \emph{Comm. Contemp. Math.}, 2, 385, 10.1142/S0219199700000190

L. Gasinski, 2006, <em>Nonlinear Analysis</em>,, Chapman & Hall/CRC

L. Gasinski, 2008, Existence and multiplicity of solutions for Neumann $p$-Laplacian type equations,, \emph{Adv. Nonlin. Studies}, 8, 843, 10.1515/ans-2008-0411

L. Gasinski, 2014, Dirichlet $(p,q)$-equations at resonance,, \emph{Discrete Contin. Dynam. Systems}, 34, 2037, 10.3934/dcds.2014.34.2037

T. Godoy, 2013, On the principal eigenvalues of some elliptic problems with large drift,, \emph{Discrete Contin. Dynam. Systems}, 33, 225, 10.3934/dcds.2013.33.225

Z. Guo, 2012, Perturbed elliptic equations with oscillatory nonlinearities,, \emph{Discrete Cont Dyn Systems}, 32, 3567, 10.3934/dcds.2012.32.3567

Z. Guo, 2003, $W^{1,p}$ versus $C^1$ local minimizers and multiplicity results for quasilinear elliptic equations,, \emph{J. Math. Anal. Appl.}, 286, 32, 10.1016/S0022-247X(03)00282-8

Z. Guo, 2011, Bifurcations of some elliptic problems with a singular nonlinearity via Morse index,, \emph{Comm. Pure. Appl. Anal.}, 10, 507, 10.3934/cpaa.2011.10.507

Shouchuan Hu, 2010, Multipcility of solutions for parametric $p$-Laplacian equations with nonlinearity concave near the origin,, \emph{Tohoku Math. J.}, 62, 137, 10.2748/tmj/1270041030

Shouchuan Hu, 2011, Nonlinear Neumann equations driven by a nonhomogeneous differential operator,, \emph{Comm. Pure Appl. Anal.}, 10, 1055, 10.3934/cpaa.2011.10.1055

Shouchuan Hu, 2012, Double resonance for Dirichlet problems with unbounded indefinite potential and combined nonlinearities,, \emph{Comm. Pure Applied Anal.}, 11, 2005, 10.3934/cpaa.2012.11.2005

Q. Jiu, 2003, Existence and multiplicity results for Dirichlet problems with $p$-Laplacian,, \emph{J. Math. Anal. Appl.}, 281, 587, 10.1016/S0022-247X(03)00165-3

E. Ko, 2013, Multiplicity results for classes of singular problems on an exterior domain,, \emph{Discrete Cont Dyn Systems}, 33, 5153, 10.3934/dcds.2013.33.5153

S. Kyritsi, 2013, Multiple solutions for nonlinear elliptic equations with asymmetric reaction term,, \emph{Discrete Cont Dyn Systems}, 33, 2469, 10.3934/dcds.2013.33.2469

G. Lieberman, 1988, Boundary regularity for solutions of degenerate elliptic equations,, \emph{Nonlin. Anal.}, 12, 1203, 10.1016/0362-546X(88)90053-3

S. Liu, 2003, Critical groups at infinity, saddle point reduction and elliptic resonant problems,, \emph{Comm. Contemp. Math.}, 5, 761, 10.1142/S0219199703001129

S. Marano, 2013, Positive solutions to a Dirichlet problem with $p$-Laplacian and concave-convex nonlinearity depending on a parameter,, \emph{Comm. Pure Appl. Anal.}, 12, 815, 10.3934/cpaa.2013.12.815

V. Moroz, 1997, Solutions of superlinear at zero elliptic equations via Morse theory,, \emph{Topol. Methods Nonl. Anal.}, 10, 387, 10.12775/TMNA.1997.039

D. Motreanu, 2014, <em>Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems</em>,, Springer, 10.1007/978-1-4614-9323-5

D. Motreanu, 2011, A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems,, \emph{Comm. Pure Appl. Anal.}, 10, 1791, 10.3934/cpaa.2011.10.1791

D. Motreanu, 2007, Existence and multiplicity of solutions for Neumann problems,, \emph{J. Diff. Equas.}, 232, 1, 10.1016/j.jde.2006.09.008

D. Motreanu, 2011, Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operator,, \emph{Proc. Amer. Math. Soc.}, 139, 3527, 10.1090/S0002-9939-2011-10884-0

D. Mugnai, 2012, Resonant nonlinear Neumann problems with indefinite weight,, \emph{Ann. Sc. Norm. Super Pisa Cl. SCI.}, 11, 729

D. Mugnai, 2014, Wang's multiplicity result for superlinear $(p,q)$-equations without the Ambrosetti-Rabinowitz condition,, \emph{Trans. Amer. Math. Soc.}, 366, 4919, 10.1090/S0002-9947-2013-06124-7

F. D. dePaiva, 2007, Multiple solutions for some elliptic equations with nonlinearity concave at the origin,, \emph{Nonlin. Anal.}, 66, 2940, 10.1016/j.na.2006.04.015

R. Palais, 1966, Homotopy theory of infinite dimensional manifolds,, \emph{Topology}, 5, 115

N. S. Papageorgiou, 2009, <em>Handbook of Applied Analysis</em>,, Springer, 10.1007/b120946

N. S. Papageorgiou, 2014, Qualitative phenomena for some classes of quasilinear elliptic equations with multiple resonance,, \emph{Appl. Math. Optim.}, 69, 393, 10.1007/s00245-013-9227-z

N. S. Papageorgiou, 2012, Positive solutions for nonlinear Neumann problems with concave and convex terms,, \emph{Positivity}, 16, 271, 10.1007/s11117-011-0124-x

N. S. Papageorgiou, On a class of parametric Neumann problems with indefinite and unbounded potential,, \emph{Forum Math.}, 10.1515/forum-2012-0042

N. S. Papageorgiou, 2014, On a parametric nonlinear Dirichlet problem with subdiffusive and equidiffusive reaction,, \emph{Adv. Nonlin. Studies}, 14, 565, 10.1515/ans-2014-0303

N. S. Papageorgiou, Resonant $(p,2)$-equations with concave terms,, \emph{Appl. Anal.}, 10.1080/00036811.2014.895332

K. Perera, 1997, Multiplicity results for some elliptic problems with concave nonlinearities,, \emph{J. Diff. Equas.}, 140, 133, 10.1006/jdeq.1997.3310

P. Pol$\acutea\brevec$ik, 2014, On the multiplicity of nonnegative solutions with a nontrivial nodal set for elliptic equations on symmetric domains,, \emph{Discrete Cont Dyn Systems}, 34, 2657, 10.3934/dcds.2014.34.2657

P. Pucci, 2007, <em>The Maximum Principle</em>,, Birkhauser

P. Sacks, 2014, Semi-linear elliptic and elliptic-parabolic equations with Wentzell boundary conditions and $L^1$-data,, \emph{Discrete Cont Dyn Systems}, 34, 761

R. Servadei, 2013, Variational methods for non-local operators of elliptic type,, \emph{Discrete Cont Dyn Systems}, 33, 2105, 10.3934/dcds.2013.33.2105

M. Struwe, 1990, <em>Variatioanl Methods</em>,, Springer-Verlag, 10.1007/978-3-662-02624-3

A. Szulkin, 2013, Infinitely many solutions for some singular elliptic problems,, \emph{Discrete Cont Dyn Systems}, 33, 321, 10.3934/dcds.2013.33.321

J. Tan, 2013, Positive solutions for non local elliptic problems,, \emph{Discrete Cont Dyn Systems}, 33, 837, 10.3934/dcds.2013.33.837

K. Thews, 1980, Nonntrivial solutions of elliptic equations at resonance,, \emph{Proc. Royal Soc. Edinburgh}, 85A, 119, 10.1017/S0308210500011732

X. Wang, 1991, Neumann problems of semilinear elliptic equations involving critical Sobolev exponents,, \emph{J. Diff. Equas.}, 93, 283, 10.1016/0022-0396(91)90014-Z

P. Winkert, 2010, $L^\infty$-estimates for nonlinear elliptic Neumann boundary value problems,, \emph{NoDEA Nonlin. Diff. Equ. Appl.}, 17, 289, 10.1007/s00030-009-0054-5

X. Yu, 2014, Liouville type theorem for nonlinear elliptic equation with general nonlinearity,, \emph{Discrete Cont Dyn Systems}, 34, 4947, 10.3934/dcds.2014.34.4947