2007, 17(1): 143-158. doi: 10.3934/dcds.2007.17.143

Positive solutions for resonant boundary value problems with the scalar p-Laplacian and nonsmooth potential

1. 

Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30072 Kraków

Received  March 2006 Revised  June 2006 Published  October 2006

In this paper we study boundary value problem with one dimensional $p$-Laplacian. Assuming complete resonance at $+\infty$ and partial resonance at $0^+$, an existence of at least one positive solution is proved. By strengthening our assumptions we can guarantee strict positivity of the obtained solution.
Citation: Leszek Gasiński. Positive solutions for resonant boundary value problems with the scalar p-Laplacian and nonsmooth potential. Discrete & Continuous Dynamical Systems - A, 2007, 17 (1) : 143-158. doi: 10.3934/dcds.2007.17.143
[1]

Scott Nollet, Frederico Xavier. Global inversion via the Palais-Smale condition. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 17-28. doi: 10.3934/dcds.2002.8.17

[2]

Antonio Azzollini. On a functional satisfying a weak Palais-Smale condition. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 1829-1840. doi: 10.3934/dcds.2014.34.1829

[3]

A. Azzollini. Erratum to: "On a functional satisfying a weak Palais-Smale condition". Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4987-4987. doi: 10.3934/dcds.2014.34.4987

[4]

Mohamed Aly Tawhid. Nonsmooth generalized complementarity as unconstrained optimization. Journal of Industrial & Management Optimization, 2010, 6 (2) : 411-423. doi: 10.3934/jimo.2010.6.411

[5]

Adam Lipowski, Bogdan Przeradzki, Katarzyna Szymańska-Dębowska. Periodic solutions to differential equations with a generalized p-Laplacian. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2593-2601. doi: 10.3934/dcdsb.2014.19.2593

[6]

Dorota Bors. Application of Mountain Pass Theorem to superlinear equations with fractional Laplacian controlled by distributed parameters and boundary data. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 29-43. doi: 10.3934/dcdsb.2018003

[7]

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

[8]

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

[9]

Everaldo S. de Medeiros, Jianfu Yang. Asymptotic behavior of solutions to a perturbed p-Laplacian problem with Neumann condition. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 595-606. doi: 10.3934/dcds.2005.12.595

[10]

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

[11]

Xian-Jun Long, Jing Quan. Optimality conditions and duality for minimax fractional programming involving nonsmooth generalized univexity. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 361-370. doi: 10.3934/naco.2011.1.361

[12]

Tomás Caraballo, Marta Herrera-Cobos, Pedro Marín-Rubio. Global attractor for a nonlocal p-Laplacian equation without uniqueness of solution. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1801-1816. doi: 10.3934/dcdsb.2017107

[13]

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

[14]

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

[15]

Julián Fernández Bonder, Leandro M. Del Pezzo. An optimization problem for the first eigenvalue of the $p-$Laplacian plus a potential. Communications on Pure & Applied Analysis, 2006, 5 (4) : 675-690. doi: 10.3934/cpaa.2006.5.675

[16]

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

[17]

Wei-Ming Ni, Xuefeng Wang. On the first positive Neumann eigenvalue. Discrete & Continuous Dynamical Systems - A, 2007, 17 (1) : 1-19. doi: 10.3934/dcds.2007.17.1

[18]

Bernd Kawohl, Jiří Horák. On the geometry of the p-Laplacian operator. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 799-813. doi: 10.3934/dcdss.2017040

[19]

Zuodong Yang, Jing Mo, Subei Li. Positive solutions of $p$-Laplacian equations with nonlinear boundary condition. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 623-636. doi: 10.3934/dcdsb.2011.16.623

[20]

Nicholas Westray, Harry Zheng. Constrained nonsmooth utility maximization on the positive real line. Mathematical Control & Related Fields, 2015, 5 (3) : 679-695. doi: 10.3934/mcrf.2015.5.679

2016 Impact Factor: 1.099

Metrics

  • PDF downloads (0)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]