• Previous Article
    Convergence versus periodicity in a single-loop positive-feedback system 1. Convergence to equilibrium
  • PROC Home
  • This Issue
  • Next Article
    Influence of the distribution component of the magnetic induction vector on rupturing capacity of vacuum switches
2011, 2011(Special): 922-930. doi: 10.3934/proc.2011.2011.922

Positive solutions for p-Laplacian equations with concave terms


Department of Mathematics, Hellenic Naval Academy, Piraeus 18539


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

Received  August 2010 Revised  February 2011 Published  October 2011

We consider a nonlinear Dirichlet problem driven by the p-Laplacian diff erential operator, with a nonlinearity concave near the origin and a nonlinear perturbation of it. We look for multiple positive solutions. We consider two distinct cases. One when the perturbation is p-linear and resonant with respect to $\lambda_1 > 0$ (the principal eigenvalue of (-$\Delta_p,W_0^(1,p)(Z)$)) at infi nity and the other when the perturbation is p-superlinear at infi nity. In both cases we obtain two positive smooth solutions. The approach is variational, coupled with the method of upper-lower solutions and with suitable truncation techniques.
Citation: Sophia Th. Kyritsi, Nikolaos S. Papageorgiou. Positive solutions for p-Laplacian equations with concave terms. Conference Publications, 2011, 2011 (Special) : 922-930. doi: 10.3934/proc.2011.2011.922

Anne Mund, Christina Kuttler, Judith Pérez-Velázquez. Existence and uniqueness of solutions to a family of semi-linear parabolic systems using coupled upper-lower solutions. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5695-5707. doi: 10.3934/dcdsb.2019102


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


Xin-Guang Yang, Marcelo J. D. Nascimento, Maurício L. Pelicer. Uniform attractors for non-autonomous plate equations with $ p $-Laplacian perturbation and critical nonlinearities. Discrete & Continuous Dynamical Systems, 2020, 40 (3) : 1937-1961. doi: 10.3934/dcds.2020100


Salvatore A. Marano, Nikolaos S. Papageorgiou. Positive solutions to a Dirichlet problem with $p$-Laplacian and concave-convex nonlinearity depending on a parameter. Communications on Pure & Applied Analysis, 2013, 12 (2) : 815-829. doi: 10.3934/cpaa.2013.12.815


Necdet Bildik, Sinan Deniz. New approximate solutions to the nonlinear Klein-Gordon equations using perturbation iteration techniques. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 503-518. doi: 10.3934/dcdss.2020028


Shouchuan Hu, Nikolas S. Papageorgiou. Positive solutions for resonant (p, q)-equations with concave terms. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2639-2656. doi: 10.3934/cpaa.2018125


Xianling Fan, Yuanzhang Zhao, Guifang Huang. Existence of solutions for the $p-$Laplacian with crossing nonlinearity. Discrete & Continuous Dynamical Systems, 2002, 8 (4) : 1019-1024. doi: 10.3934/dcds.2002.8.1019


Angelo Favini, Alfredo Lorenzi, Hiroki Tanabe, Atsushi Yagi. An $L^p$-approach to singular linear parabolic equations with lower order terms. Discrete & Continuous Dynamical Systems, 2008, 22 (4) : 989-1008. doi: 10.3934/dcds.2008.22.989


Lucas C. F. Ferreira, Elder J. Villamizar-Roa. On the heat equation with concave-convex nonlinearity and initial data in weak-$L^p$ spaces. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1715-1732. doi: 10.3934/cpaa.2011.10.1715


Mingqi Xiang, Binlin Zhang. A critical fractional p-Kirchhoff type problem involving discontinuous nonlinearity. Discrete & Continuous Dynamical Systems - S, 2019, 12 (2) : 413-433. doi: 10.3934/dcdss.2019027


R. S. Johnson. A selection of nonlinear problems in water waves, analysed by perturbation-parameter techniques. Communications on Pure & Applied Analysis, 2012, 11 (4) : 1497-1522. doi: 10.3934/cpaa.2012.11.1497


D. Motreanu, Donal O'Regan, Nikolaos S. Papageorgiou. A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1791-1816. doi: 10.3934/cpaa.2011.10.1791


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


John Boyd. Strongly nonlinear perturbation theory for solitary waves and bions. Evolution Equations & Control Theory, 2019, 8 (1) : 1-29. doi: 10.3934/eect.2019001


Guowei Dai. Bifurcation and one-sign solutions of the $p$-Laplacian involving a nonlinearity with zeros. Discrete & Continuous Dynamical Systems, 2016, 36 (10) : 5323-5345. doi: 10.3934/dcds.2016034


Trad Alotaibi, D. D. Hai, R. Shivaji. Existence and nonexistence of positive radial solutions for a class of $p$-Laplacian superlinear problems with nonlinear boundary conditions. Communications on Pure & Applied Analysis, 2020, 19 (9) : 4655-4666. doi: 10.3934/cpaa.2020131


K. D. Chu, D. D. Hai. Positive solutions for the one-dimensional singular superlinear $ p $-Laplacian problem. Communications on Pure & Applied Analysis, 2020, 19 (1) : 241-252. doi: 10.3934/cpaa.2020013


Ryo Ikehata, Marina Soga. Asymptotic profiles for a strongly damped plate equation with lower order perturbation. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1759-1780. doi: 10.3934/cpaa.2015.14.1759


Roberta Fabbri, Carmen Núñez, Ana M. Sanz. A perturbation theorem for linear Hamiltonian systems with bounded orbits. Discrete & Continuous Dynamical Systems, 2005, 13 (3) : 623-635. doi: 10.3934/dcds.2005.13.623


Ruotian Gao, Wenxun Xing. Robust sensitivity analysis for linear programming with ellipsoidal perturbation. Journal of Industrial & Management Optimization, 2020, 16 (4) : 2029-2044. doi: 10.3934/jimo.2019041

 Impact Factor: 


  • PDF downloads (56)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]