American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Existence of nontrivial solutions for some elliptic equations with supercritical nonlinearity in exterior domains
  • DCDS Home
  • This Issue
  • Next Article
    Boundary blow-up solutions with interior layers and spikes in a bistable problem
May  2007, 19(2): 299-321. doi: 10.3934/dcds.2007.19.299

Vector p-Laplacian like operators, pseudo-eigenvalues, and bifurcation

Marta García-Huidobro 1, , Raul Manásevich 2, and  J. R. Ward 3,

1. 

Department of Mathematics, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago
2. 

Centro de Modelamiento Matemático and Departamento de Ingenieria Matemática, F.C.F.M, Universidad de Chile, Casilla 170, Correo 3, Santiago
3. 

Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, 35294-1170, United States

Received  November 2005 Revised  November 2006 Published  July 2007

Boundary value problems for systems of ordinary differential equations are studied. These systems involve asymptotically homogeneous operators. Leray-Schauder indices are calculated for these operators and the concept of pseudo-eigenvalue is defined. The existence of nontrivial solutions is studied. Conditions for bifurcation, from either zero or infinity, at the pseudo-eigenvalues are given.
Keywords: bifurcation, Asymptotically homogeneous operators, nonlinear boundary value problems, p-Laplacian systems, pseudo-eigenvalue..
Mathematics Subject Classification: 34A34, 34B15, 34C23, 47J05, 47H11, 47J10, 47J1.
Citation: Marta García-Huidobro, Raul Manásevich, J. R. Ward. Vector p-Laplacian like operators, pseudo-eigenvalues, and bifurcation. Discrete & Continuous Dynamical Systems, 2007, 19 (2) : 299-321. doi: 10.3934/dcds.2007.19.299
[1]

Kanishka Perera, Andrzej Szulkin. p-Laplacian problems where the nonlinearity crosses an eigenvalue. Discrete & Continuous Dynamical Systems, 2005, 13 (3) : 743-753. doi: 10.3934/dcds.2005.13.743
[2]

Leszek Gasiński. Positive solutions for resonant boundary value problems with the scalar p-Laplacian and nonsmooth potential. Discrete & Continuous Dynamical Systems, 2007, 17 (1) : 143-158. doi: 10.3934/dcds.2007.17.143
[3]

Eun Kyoung Lee, R. Shivaji, Inbo Sim, Byungjae Son. Analysis of positive solutions for a class of semipositone p-Laplacian problems with nonlinear boundary conditions. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1139-1154. doi: 10.3934/cpaa.2019055
[4]

Yansheng Zhong, Yongqing Li. On a p-Laplacian eigenvalue problem with supercritical exponent. Communications on Pure & Applied Analysis, 2019, 18 (1) : 227-236. doi: 10.3934/cpaa.2019012
[5]

Michael E. Filippakis, Nikolaos S. Papageorgiou. Existence and multiplicity of positive solutions for nonlinear boundary value problems driven by the scalar $p$-Laplacian. Communications on Pure & Applied Analysis, 2004, 3 (4) : 729-756. doi: 10.3934/cpaa.2004.3.729
[6]

Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad. Nonlinear singular $ p $ -Laplacian boundary value problems in the frame of conformable derivative. Discrete & Continuous Dynamical Systems - S, 2021, 14 (10) : 3497-3528. doi: 10.3934/dcdss.2020442
[7]

Stanislav Nikolaevich Antontsev, Serik Ersultanovich Aitzhanov, Guzel Rashitkhuzhakyzy Ashurova. An inverse problem for the pseudo-parabolic equation with p-Laplacian. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021005
[8]

J. Ángel Cid, Pedro J. Torres. Solvability for some boundary value problems with $\phi$-Laplacian operators. Discrete & Continuous Dynamical Systems, 2009, 23 (3) : 727-732. doi: 10.3934/dcds.2009.23.727
[9]

Genni Fragnelli, Dimitri Mugnai, Nikolaos S. Papageorgiou. Robin problems for the p-Laplacian with gradient dependence. Discrete & Continuous Dynamical Systems - S, 2019, 12 (2) : 287-295. doi: 10.3934/dcdss.2019020
[10]

Mihai Mihăilescu, Julio D. Rossi. Monotonicity with respect to $ p $ of the First Nontrivial Eigenvalue of the $ p $-Laplacian with Homogeneous Neumann Boundary Conditions. Communications on Pure & Applied Analysis, 2020, 19 (9) : 4363-4371. doi: 10.3934/cpaa.2020198
[11]

Giuseppina Barletta, Roberto Livrea, Nikolaos S. Papageorgiou. A nonlinear eigenvalue problem for the periodic scalar $p$-Laplacian. Communications on Pure & Applied Analysis, 2014, 13 (3) : 1075-1086. doi: 10.3934/cpaa.2014.13.1075
[12]

Dimitri Mugnai. Bounce on a p-Laplacian. Communications on Pure & Applied Analysis, 2003, 2 (3) : 371-379. doi: 10.3934/cpaa.2003.2.371
[13]

VicenŢiu D. RǍdulescu, Somayeh Saiedinezhad. A nonlinear eigenvalue problem with $ p(x) $-growth and generalized Robin boundary value condition. Communications on Pure & Applied Analysis, 2018, 17 (1) : 39-52. doi: 10.3934/cpaa.2018003
[14]

Lingyu Jin, Yan Li. A Hopf's lemma and the boundary regularity for the fractional p-Laplacian. Discrete & Continuous Dynamical Systems, 2019, 39 (3) : 1477-1495. doi: 10.3934/dcds.2019063
[15]

Francisco Odair de Paiva, Humberto Ramos Quoirin. Resonance and nonresonance for p-Laplacian problems with weighted eigenvalues conditions. Discrete & Continuous Dynamical Systems, 2009, 25 (4) : 1219-1227. doi: 10.3934/dcds.2009.25.1219
[16]

Petru Jebelean. Infinitely many solutions for ordinary $p$-Laplacian systems with nonlinear boundary conditions. Communications on Pure & Applied Analysis, 2008, 7 (2) : 267-275. doi: 10.3934/cpaa.2008.7.267
[17]

Shun Uchida. Solvability of doubly nonlinear parabolic equation with p-laplacian. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021033
[18]

J. R. L. Webb. Uniqueness of the principal eigenvalue in nonlocal boundary value problems. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 177-186. doi: 10.3934/dcdss.2008.1.177
[19]

Meiqiang Feng, Yichen Zhang. Positive solutions of singular multiparameter p-Laplacian elliptic systems. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021083
[20]

Maya Chhetri, D. D. Hai, R. Shivaji. On positive solutions for classes of p-Laplacian semipositone systems. Discrete & Continuous Dynamical Systems, 2003, 9 (4) : 1063-1071. doi: 10.3934/dcds.2003.9.1063

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (45)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences