American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Completely monotonic functions involving divided differences of the di- and tri-gamma functions and some applications
  • CPAA Home
  • This Issue
  • Next Article
    On synchronization of oscillations of two coupled Berger plates with nonlinear interior damping
November  2009, 8(6): 1957-1974. doi: 10.3934/cpaa.2009.8.1957

Multiple solutions for nonlinear coercive Neumann problems

Sophia Th. Kyritsi 1, and  Nikolaos S. Papageorgiou 2,

1. 

Department of Mathematics, Hellenic Naval Academy, Piraeus 18539, Greece
2. 

Department of Mathematics, National Technical University, Zografou Campus, Athens 15780

Received  June 2008 Revised  February 2009 Published  August 2009

In this paper we deal with a nonlinear Neumann problem driven by the $p$--Laplacian and with a potential function which asymptotically at infinity is $p$--linear. Using variational methods based on critical point theory coupled with suitable truncation techniques, we prove a theorem establishing the existence of at least three nontrivial smooth solutions for the Neumann problem. For the semilinear case (i.e., $p=2$) using Morse theory, we produce one more nontrivial smooth solution.
Keywords: p–Laplacian, critical groups., Morse theory, linking theorem, three nontrivial smooth solutions, local minimizer, second deformation theorem.
Mathematics Subject Classification: 35J25, 35J70, 58E05, 58J7.
Citation: Sophia Th. Kyritsi, Nikolaos S. Papageorgiou. Multiple solutions for nonlinear coercive Neumann problems. Communications on Pure and Applied Analysis, 2009, 8 (6) : 1957-1974. doi: 10.3934/cpaa.2009.8.1957
[1]

Leszek Gasiński, Nikolaos S. Papageorgiou. Three nontrivial solutions for periodic problems with the $p$-Laplacian and a $p$-superlinear nonlinearity. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1421-1437. doi: 10.3934/cpaa.2009.8.1421
[2]

Jijiang Sun, Shiwang Ma. Nontrivial solutions for Kirchhoff type equations via Morse theory. Communications on Pure and Applied Analysis, 2014, 13 (2) : 483-494. doi: 10.3934/cpaa.2014.13.483
[3]

Francesca Colasuonno, Fausto Ferrari. The Soap Bubble Theorem and a $ p $-Laplacian overdetermined problem. Communications on Pure and Applied Analysis, 2020, 19 (2) : 983-1000. doi: 10.3934/cpaa.2020045
[4]

Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure and Applied Analysis, 2021, 20 (1) : 449-465. doi: 10.3934/cpaa.2020276
[5]

Qiong Meng, X. H. Tang. Multiple solutions of second-order ordinary differential equation via Morse theory. Communications on Pure and Applied Analysis, 2012, 11 (3) : 945-958. doi: 10.3934/cpaa.2012.11.945
[6]

Robert Stegliński. On homoclinic solutions for a second order difference equation with p-Laplacian. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 487-492. doi: 10.3934/dcdsb.2018033
[7]

John R. Graef, Lingju Kong, Min Wang. Existence of homoclinic solutions for second order difference equations with $p$-laplacian. Conference Publications, 2015, 2015 (special) : 533-539. doi: 10.3934/proc.2015.0533
[8]

Massimiliano Ferrara, Giovanni Molica Bisci, Binlin Zhang. Existence of weak solutions for non-local fractional problems via Morse theory. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2483-2499. doi: 10.3934/dcdsb.2014.19.2483
[9]

Gongbao Li, Tao Yang. Improved Sobolev inequalities involving weighted Morrey norms and the existence of nontrivial solutions to doubly critical elliptic systems involving fractional Laplacian and Hardy terms. Discrete and Continuous Dynamical Systems - S, 2021, 14 (6) : 1945-1966. doi: 10.3934/dcdss.2020469
[10]

Xinjing Wang. Liouville type theorem for Fractional Laplacian system. Communications on Pure and Applied Analysis, 2020, 19 (11) : 5253-5268. doi: 10.3934/cpaa.2020236
[11]

Edcarlos D. Silva, Jefferson S. Silva. Multiplicity of solutions for critical quasilinear Schrödinger equations using a linking structure. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5441-5470. doi: 10.3934/dcds.2020234
[12]

M. Grossi, P. Magrone, M. Matzeu. Linking type solutions for elliptic equations with indefinite nonlinearities up to the critical growth. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 703-718. doi: 10.3934/dcds.2001.7.703
[13]

Anran Li, Jiabao Su. Multiple nontrivial solutions to a $p$-Kirchhoff equation. Communications on Pure and Applied Analysis, 2016, 15 (1) : 91-102. doi: 10.3934/cpaa.2016.15.91
[14]

Jan Boman. A local uniqueness theorem for weighted Radon transforms. Inverse Problems and Imaging, 2010, 4 (4) : 631-637. doi: 10.3934/ipi.2010.4.631
[15]

Magdalena Nockowska-Rosiak, Piotr Hachuła, Ewa Schmeidel. Existence of uncountably many asymptotically constant solutions to discrete nonlinear three-dimensional system with $p$-Laplacian. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 369-375. doi: 10.3934/dcdsb.2018025
[16]

Brandon Seward. Krieger's finite generator theorem for actions of countable groups Ⅱ. Journal of Modern Dynamics, 2019, 15: 1-39. doi: 10.3934/jmd.2019012
[17]

Daniele Mundici. The Haar theorem for lattice-ordered abelian groups with order-unit. Discrete and Continuous Dynamical Systems, 2008, 21 (2) : 537-549. doi: 10.3934/dcds.2008.21.537
[18]

Luciana A. Alves, Luiz A. B. San Martin. Multiplicative ergodic theorem on flag bundles of semi-simple Lie groups. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1247-1273. doi: 10.3934/dcds.2013.33.1247
[19]

Yinbin Deng, Yi Li, Wei Shuai. Existence of solutions for a class of p-Laplacian type equation with critical growth and potential vanishing at infinity. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 683-699. doi: 10.3934/dcds.2016.36.683
[20]

Nicholas J. Kass, Mohammad A. Rammaha. Local and global existence of solutions to a strongly damped wave equation of the $ p $-Laplacian type. Communications on Pure and Applied Analysis, 2018, 17 (4) : 1449-1478. doi: 10.3934/cpaa.2018070

2021 Impact Factor: 1.273

Tools

Metrics

  • PDF downloads (77)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy