-
Previous Article
Well-posedness and ill-posedness results for the Novikov-Veselov equation
- CPAA Home
- This Issue
-
Next Article
Nonexistence of positive solutions for polyharmonic systems in $\mathbb{R}^N_+$
On Compactness Conditions for the $p$-Laplacian
1. | Department of Mathematics, University of West Bohemia, Univerzitní 8, 306 14 Pilsen, Czech Republic |
References:
[1] |
J. Anane, Simplicité et isolation de la première valeur propre du $p$-laplacien avec poids, Comptes Rendus Acad.Sci. Paris Srie I, (1987). |
[2] |
P. Drábek, P. Girg, P. Takáč and M. Ulm, The Fredholm alternative for the $p$-Laplacian: bifurcation from infinity, existence and multiplicity, Indiana Univ. Math. J., (2004).
doi: 10.1512/iumj.2004.53.2396. |
[3] |
P. Drábek and J. Milota, Methods of Nonlinear Analysis, Birkhäuser, 2013.
doi: 10.1007/978-3-0348-0387-8. |
[4] |
P. Drábek and P. Takáč , Poincaré inequality and Palais-Smale condition for the $p$-Laplacian, Calc. Var., (2007).
doi: 10.1007/s00526-006-0055-8. |
[5] |
A. R. El Amrouss, Critical Point Theorems and Applications to Differential Equations, Acta Math. Sinica, English Series, (2005).
doi: 10.1007/s10114-004-0442-z. |
[6] |
J. Fleckinger and P. Takáč, An improved Poincaré inequality and the $p$-Laplacian at resonance for $p>2$, Adv.Differ Equ., (2002). |
[7] |
P. Takáč, On the Fredholm alternative for the $p$-Laplacian at the first eigenvalue, Indiana Univ. Math. J., (2002).
doi: 10.1512/iumj.2002.51.2156. |
[8] |
P. Takáč, On the number and structure of solutions for a Fredholm alternative with the $p$-Laplacian, J. Differ. Equ., (2002).
doi: 10.1006/jdeq.2002.4173. |
show all references
References:
[1] |
J. Anane, Simplicité et isolation de la première valeur propre du $p$-laplacien avec poids, Comptes Rendus Acad.Sci. Paris Srie I, (1987). |
[2] |
P. Drábek, P. Girg, P. Takáč and M. Ulm, The Fredholm alternative for the $p$-Laplacian: bifurcation from infinity, existence and multiplicity, Indiana Univ. Math. J., (2004).
doi: 10.1512/iumj.2004.53.2396. |
[3] |
P. Drábek and J. Milota, Methods of Nonlinear Analysis, Birkhäuser, 2013.
doi: 10.1007/978-3-0348-0387-8. |
[4] |
P. Drábek and P. Takáč , Poincaré inequality and Palais-Smale condition for the $p$-Laplacian, Calc. Var., (2007).
doi: 10.1007/s00526-006-0055-8. |
[5] |
A. R. El Amrouss, Critical Point Theorems and Applications to Differential Equations, Acta Math. Sinica, English Series, (2005).
doi: 10.1007/s10114-004-0442-z. |
[6] |
J. Fleckinger and P. Takáč, An improved Poincaré inequality and the $p$-Laplacian at resonance for $p>2$, Adv.Differ Equ., (2002). |
[7] |
P. Takáč, On the Fredholm alternative for the $p$-Laplacian at the first eigenvalue, Indiana Univ. Math. J., (2002).
doi: 10.1512/iumj.2002.51.2156. |
[8] |
P. Takáč, On the number and structure of solutions for a Fredholm alternative with the $p$-Laplacian, J. Differ. Equ., (2002).
doi: 10.1006/jdeq.2002.4173. |
[1] |
Antonio Azzollini. On a functional satisfying a weak Palais-Smale condition. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 1829-1840. doi: 10.3934/dcds.2014.34.1829 |
[2] |
Scott Nollet, Frederico Xavier. Global inversion via the Palais-Smale condition. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 17-28. doi: 10.3934/dcds.2002.8.17 |
[3] |
A. Azzollini. Erratum to: "On a functional satisfying a weak Palais-Smale condition". Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4987-4987. doi: 10.3934/dcds.2014.34.4987 |
[4] |
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 and Applied Analysis, 2004, 3 (4) : 729-756. doi: 10.3934/cpaa.2004.3.729 |
[5] |
John R. Graef, Lingju Kong. Uniqueness and parameter dependence of positive solutions of third order boundary value problems with $p$-laplacian. Conference Publications, 2011, 2011 (Special) : 515-522. doi: 10.3934/proc.2011.2011.515 |
[6] |
Leszek Gasiński. Positive solutions for resonant boundary value problems with the scalar p-Laplacian and nonsmooth potential. Discrete and Continuous Dynamical Systems, 2007, 17 (1) : 143-158. doi: 10.3934/dcds.2007.17.143 |
[7] |
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 and Continuous Dynamical Systems - S, 2021, 14 (10) : 3497-3528. doi: 10.3934/dcdss.2020442 |
[8] |
Zuodong Yang, Jing Mo, Subei Li. Positive solutions of $p$-Laplacian equations with nonlinear boundary condition. Discrete and Continuous Dynamical Systems - B, 2011, 16 (2) : 623-636. doi: 10.3934/dcdsb.2011.16.623 |
[9] |
Agnid Banerjee, Nicola Garofalo. On the Dirichlet boundary value problem for the normalized $p$-laplacian evolution. Communications on Pure and Applied Analysis, 2015, 14 (1) : 1-21. doi: 10.3934/cpaa.2015.14.1 |
[10] |
R. Kannan, S. Seikkala. Existence of solutions to some Phi-Laplacian boundary value problems. Conference Publications, 2001, 2001 (Special) : 211-217. doi: 10.3934/proc.2001.2001.211 |
[11] |
J. Ángel Cid, Pedro J. Torres. Solvability for some boundary value problems with $\phi$-Laplacian operators. Discrete and Continuous Dynamical Systems, 2009, 23 (3) : 727-732. doi: 10.3934/dcds.2009.23.727 |
[12] |
Nicola Abatangelo, Sven Jarohs, Alberto Saldaña. Positive powers of the Laplacian: From hypersingular integrals to boundary value problems. Communications on Pure and Applied Analysis, 2018, 17 (3) : 899-922. doi: 10.3934/cpaa.2018045 |
[13] |
Juan Campos, Rafael Obaya, Massimo Tarallo. Recurrent equations with sign and Fredholm alternative. Discrete and Continuous Dynamical Systems - S, 2016, 9 (4) : 959-977. doi: 10.3934/dcdss.2016036 |
[14] |
Umberto De Maio, Peter I. Kogut, Gabriella Zecca. On optimal $ L^1 $-control in coefficients for quasi-linear Dirichlet boundary value problems with $ BMO $-anisotropic $ p $-Laplacian. Mathematical Control and Related Fields, 2020, 10 (4) : 827-854. doi: 10.3934/mcrf.2020021 |
[15] |
Wen Tan. The regularity of pullback attractor for a non-autonomous p-Laplacian equation with dynamical boundary condition. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 529-546. doi: 10.3934/dcdsb.2018194 |
[16] |
VicenŢiu D. RǍdulescu, Somayeh Saiedinezhad. A nonlinear eigenvalue problem with $ p(x) $-growth and generalized Robin boundary value condition. Communications on Pure and Applied Analysis, 2018, 17 (1) : 39-52. doi: 10.3934/cpaa.2018003 |
[17] |
Anna Mercaldo, Julio D. Rossi, Sergio Segura de León, Cristina Trombetti. Behaviour of $p$--Laplacian problems with Neumann boundary conditions when $p$ goes to 1. Communications on Pure and Applied Analysis, 2013, 12 (1) : 253-267. doi: 10.3934/cpaa.2013.12.253 |
[18] |
Lorenzo Brasco, Enea Parini, Marco Squassina. Stability of variational eigenvalues for the fractional $p-$Laplacian. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 1813-1845. doi: 10.3934/dcds.2016.36.1813 |
[19] |
Alberto Cabada, J. Ángel Cid. Heteroclinic solutions for non-autonomous boundary value problems with singular $\Phi$-Laplacian operators. Conference Publications, 2009, 2009 (Special) : 118-122. doi: 10.3934/proc.2009.2009.118 |
[20] |
Youngmok Jeon, Dongwook Shin. Immersed hybrid difference methods for elliptic boundary value problems by artificial interface conditions. Electronic Research Archive, 2021, 29 (5) : 3361-3382. doi: 10.3934/era.2021043 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]