Positive solutions for <em>p</em>-Laplacian equations with concave terms

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

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

1.	Department of Mathematics, Hellenic Naval Academy, Piraeus 18539
2.	Department of Mathematics, National Technical University, Zografou Campus, Athens 15780

Received August 2010 Revised February 2011 Published October 2011

Abstract
Related Papers

We consider a nonlinear Dirichlet problem driven by the p-Laplacian differential 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 infinity and the other when the perturbation is p-superlinear at infinity. 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.

Keywords: p-superlinear perturbation, Concave nonlinearity, critical point theory., truncation techniques, p-linear perturbation, upper-lower solutions.

Mathematics Subject Classification: 35J65, 35J7.

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

[1]	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
[2]	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
[3]	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 - A, 2020, 40 (3) : 1937-1961. doi: 10.3934/dcds.2020100
[4]	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
[5]	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
[6]	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
[7]	Xianling Fan, Yuanzhang Zhao, Guifang Huang. Existence of solutions for the $p-$Laplacian with crossing nonlinearity. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 1019-1024. doi: 10.3934/dcds.2002.8.1019
[8]	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 - A, 2008, 22 (4) : 989-1008. doi: 10.3934/dcds.2008.22.989
[9]	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
[10]	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
[11]	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
[12]	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
[13]	Guowei Dai. Bifurcation and one-sign solutions of the $p$-Laplacian involving a nonlinearity with zeros. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5323-5345. doi: 10.3934/dcds.2016034
[14]	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
[15]	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
[16]	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
[17]	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
[18]	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
[19]	Chunyan Ji, Xue Yang, Yong Li. Periodic solutions for SDEs through upper and lower solutions. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020122
[20]	Roberta Fabbri, Carmen Núñez, Ana M. Sanz. A perturbation theorem for linear Hamiltonian systems with bounded orbits. Discrete & Continuous Dynamical Systems - A, 2005, 13 (3) : 623-635. doi: 10.3934/dcds.2005.13.623

Impact Factor:

Tools

Metrics

Other articles
by authors

on AIMS
Sophia Th. Kyritsi Nikolaos S. Papageorgiou
on Google Scholar
Sophia Th. Kyritsi Nikolaos S. Papageorgiou

[Back to Top]