# American Institute of Mathematical Sciences

• 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

 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.
Citation: Sophia Th. Kyritsi, Nikolaos S. Papageorgiou. Multiple solutions for nonlinear coercive Neumann problems. Communications on Pure &amp; 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] 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 & 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 & 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 & 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 & Continuous Dynamical Systems - B, 2014, 19 (8) : 2483-2499. doi: 10.3934/dcdsb.2014.19.2483 [9] Xinjing Wang. Liouville type theorem for Fractional Laplacian system. Communications on Pure & Applied Analysis, 2020, 19 (11) : 5253-5268. doi: 10.3934/cpaa.2020236 [10] 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 & Continuous Dynamical Systems - S, 2021, 14 (6) : 1945-1966. doi: 10.3934/dcdss.2020469 [11] Edcarlos D. Silva, Jefferson S. Silva. Multiplicity of solutions for critical quasilinear Schrödinger equations using a linking structure. Discrete & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & Applied Analysis, 2018, 17 (4) : 1449-1478. doi: 10.3934/cpaa.2018070

2020 Impact Factor: 1.916