American Institute of Mathematical Sciences

Advanced
September  2003, 2(3): 411-423. doi: 10.3934/cpaa.2003.2.411

Positive solutions of superlinear boundary value problems with singular indefinite weight

M. Gaudenzi 1, , P. Habets 2, and  F. Zanolin 3,

1. 

Dipartimento di Finanzia dell'Impresa e dei Mercati Finanziari, Università, Via Tomadini 30, I-33100 Udine, Italy
2. 

Institut de Mathématiques Pures et Appliquées, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
3. 

Dipartimento di Matematica e Informatica, Università, Via Delle Scienze 206, I-33100 Udine, Italy

Received  July 2002 Revised  March 2003 Published  June 2003

In the present paper, we propose a method to deal with non-ordered lower and upper solutions in the case of ODE's with singular coefficients. As an application, we study the existence of positive solutions for a two-point boundary value problem on ]0,1[ associated to the equation $u'' + a(t) g(u) = 0,$ where the function $g: \quad \mathbb R^+\to \mathbb R^+$ is continuous with superlinear growth at infinity and the weight $a(t)$ changes sign as well as it may present some singularities at $t=0$ or $t= 1.$
Keywords: singular coe±cients., Positive solutions, indefinite weight, superlinear equations.
Mathematics Subject Classification: 34B15, 34L4.
Citation: M. Gaudenzi, P. Habets, F. Zanolin. Positive solutions of superlinear boundary value problems with singular indefinite weight. Communications on Pure and Applied Analysis, 2003, 2 (3) : 411-423. doi: 10.3934/cpaa.2003.2.411
[1]

Guglielmo Feltrin. Positive subharmonic solutions to superlinear ODEs with indefinite weight. Discrete and Continuous Dynamical Systems - S, 2018, 11 (2) : 257-277. doi: 10.3934/dcdss.2018014
[2]

Guglielmo Feltrin. Existence of positive solutions of a superlinear boundary value problem with indefinite weight. Conference Publications, 2015, 2015 (special) : 436-445. doi: 10.3934/proc.2015.0436
[3]

Alberto Boscaggin, Maurizio Garrione. Positive solutions to indefinite Neumann problems when the weight has positive average. Discrete and Continuous Dynamical Systems, 2016, 36 (10) : 5231-5244. doi: 10.3934/dcds.2016028
[4]

Zuzana Došlá, Mauro Marini, Serena Matucci. Global Kneser solutions to nonlinear equations with indefinite weight. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 3297-3308. doi: 10.3934/dcdsb.2018252
[5]

Ryuji Kajikiya, Daisuke Naimen. Two sequences of solutions for indefinite superlinear-sublinear elliptic equations with nonlinear boundary conditions. Communications on Pure and Applied Analysis, 2014, 13 (4) : 1593-1612. doi: 10.3934/cpaa.2014.13.1593
[6]

K. D. Chu, D. D. Hai. Positive solutions for the one-dimensional singular superlinear $ p $-Laplacian problem. Communications on Pure and Applied Analysis, 2020, 19 (1) : 241-252. doi: 10.3934/cpaa.2020013
[7]

Uriel Kaufmann, Humberto Ramos Quoirin, Kenichiro Umezu. A curve of positive solutions for an indefinite sublinear Dirichlet problem. Discrete and Continuous Dynamical Systems, 2020, 40 (2) : 817-845. doi: 10.3934/dcds.2020063
[8]

Pablo Amster, Manuel Zamora. Periodic solutions for indefinite singular equations with singularities in the spatial variable and non-monotone nonlinearity. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 4819-4835. doi: 10.3934/dcds.2018211
[9]

Ying-Chieh Lin, Tsung-Fang Wu. On the semilinear fractional elliptic equations with singular weight functions. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 2067-2084. doi: 10.3934/dcdsb.2020325
[10]

Xiaomei Sun, Wenyi Chen. Positive solutions for singular elliptic equations with critical Hardy-Sobolev exponent. Communications on Pure and Applied Analysis, 2011, 10 (2) : 527-540. doi: 10.3934/cpaa.2011.10.527
[11]

Julián López-Góme, Andrea Tellini, F. Zanolin. High multiplicity and complexity of the bifurcation diagrams of large solutions for a class of superlinear indefinite problems. Communications on Pure and Applied Analysis, 2014, 13 (1) : 1-73. doi: 10.3934/cpaa.2014.13.1
[12]

Jiaquan Liu, Yuxia Guo, Pingan Zeng. Relationship of the morse index and the $L^\infty$ bound of solutions for a strongly indefinite differential superlinear system. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 107-119. doi: 10.3934/dcds.2006.16.107
[13]

Genni Fragnelli, Dimitri Mugnai, Nikolaos S. Papageorgiou. Positive and nodal solutions for parametric nonlinear Robin problems with indefinite potential. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6133-6166. doi: 10.3934/dcds.2016068
[14]

Rushun Tian, Zhi-Qiang Wang. Bifurcation results on positive solutions of an indefinite nonlinear elliptic system. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 335-344. doi: 10.3934/dcds.2013.33.335
[15]

Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš. Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2589-2618. doi: 10.3934/dcds.2017111
[16]

Vladimir Lubyshev. Precise range of the existence of positive solutions of a nonlinear, indefinite in sign Neumann problem. Communications on Pure and Applied Analysis, 2009, 8 (3) : 999-1018. doi: 10.3934/cpaa.2009.8.999
[17]

Guglielmo Feltrin, Elisa Sovrano, Andrea Tellini. On the number of positive solutions to an indefinite parameter-dependent Neumann problem. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 21-71. doi: 10.3934/dcds.2021107
[18]

Yuxia Guo, Shaolong Peng. Monotonicity and nonexistence of positive solutions for pseudo-relativistic equation with indefinite nonlinearity. Communications on Pure and Applied Analysis, 2022, 21 (5) : 1637-1648. doi: 10.3934/cpaa.2022037
[19]

Julián López-Gómez, Marcela Molina-Meyer, Andrea Tellini. Spiraling bifurcation diagrams in superlinear indefinite problems. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1561-1588. doi: 10.3934/dcds.2015.35.1561
[20]

Alfonso Castro, Jorge Cossio, Sigifredo Herrón, Carlos Vélez. Infinitely many radial solutions for a $ p $-Laplacian problem with indefinite weight. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4805-4821. doi: 10.3934/dcds.2021058

2021 Impact Factor: 1.273

Tools

Metrics

  • PDF downloads (128)
  • HTML views (0)
  • Cited by (10)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy