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 & 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 & 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 & 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 & Applied Analysis, 2020, 19 (2) : 983-1000. doi: 10.3934/cpaa.2020045
[4]

Robert Stegliński. On homoclinic solutions for a second order difference equation with p-Laplacian. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 487-492. doi: 10.3934/dcdsb.2018033
[5]

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
[6]

Qiong Meng, X. H. Tang. Multiple solutions of second-order ordinary differential equation via Morse theory. Communications on Pure & Applied Analysis, 2012, 11 (3) : 945-958. doi: 10.3934/cpaa.2012.11.945
[7]

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

Anran Li, Jiabao Su. Multiple nontrivial solutions to a $p$-Kirchhoff equation. Communications on Pure & Applied Analysis, 2016, 15 (1) : 91-102. doi: 10.3934/cpaa.2016.15.91
[9]

M. Grossi, P. Magrone, M. Matzeu. Linking type solutions for elliptic equations with indefinite nonlinearities up to the critical growth. Discrete & Continuous Dynamical Systems - A, 2001, 7 (4) : 703-718. doi: 10.3934/dcds.2001.7.703
[10]

Jan Boman. A local uniqueness theorem for weighted Radon transforms. Inverse Problems & Imaging, 2010, 4 (4) : 631-637. doi: 10.3934/ipi.2010.4.631
[11]

Magdalena Nockowska-Rosiak, Piotr Hachuła, Ewa Schmeidel. Existence of uncountably many asymptotically constant solutions to discrete nonlinear three-dimensional system with $p$-Laplacian. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 369-375. doi: 10.3934/dcdsb.2018025
[12]

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 & Continuous Dynamical Systems - A, 2016, 36 (2) : 683-699. doi: 10.3934/dcds.2016.36.683
[13]

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 & Applied Analysis, 2018, 17 (4) : 1449-1478. doi: 10.3934/cpaa.2018070
[14]

Daniele Mundici. The Haar theorem for lattice-ordered abelian groups with order-unit. Discrete & Continuous Dynamical Systems - A, 2008, 21 (2) : 537-549. doi: 10.3934/dcds.2008.21.537
[15]

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

Nguyen Lam, Guozhen Lu. Existence of nontrivial solutions to Polyharmonic equations with subcritical and critical exponential growth. Discrete & Continuous Dynamical Systems - A, 2012, 32 (6) : 2187-2205. doi: 10.3934/dcds.2012.32.2187
[18]

Ting Guo, Xianhua Tang, Qi Zhang, Zu Gao. Nontrivial solutions for the choquard equation with indefinite linear part and upper critical exponent. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1563-1579. doi: 10.3934/cpaa.2020078
[19]

Oliver Díaz-Espinosa, Rafael de la Llave. Renormalization and central limit theorem for critical dynamical systems with weak external noise. Journal of Modern Dynamics, 2007, 1 (3) : 477-543. doi: 10.3934/jmd.2007.1.477
[20]

Zhenjie Li, Ze Cheng, Dongsheng Li. The Liouville type theorem and local regularity results for nonlinear differential and integral systems. Communications on Pure & Applied Analysis, 2015, 14 (2) : 565-576. doi: 10.3934/cpaa.2015.14.565

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (15)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences