March  2010, 9(2): 563-581. doi: 10.3934/cpaa.2010.9.563

Semi-positone nonlocal boundary value problems of arbitrary order

1. 

Department of Mathematics, University of Glasgow, Glasgow G12 8QW

2. 

Dipartimento di Matematica, Università della Calabria, 87036 Arcavacata di Rende, Cosenza

Received  December 2008 Revised  August 2009 Published  December 2009

We give a unified approach to the study of existence of multiple positive solutions for semi-positone boundary value problems of arbitrary order. We cover local and nonlocal boundary conditions. Our nonlocal boundary conditions are quite general, they involve positive linear functionals on the space $C[0,1]$, given by Stieltjes integrals. With our general theory, we can, for the first time in semi-positone problems, allow any number of the boundary conditions to be nonlocal.
Citation: J. R. L. Webb, Gennaro Infante. Semi-positone nonlocal boundary value problems of arbitrary order. Communications on Pure and Applied Analysis, 2010, 9 (2) : 563-581. doi: 10.3934/cpaa.2010.9.563
[1]

K. Q. Lan. Positive solutions of semi-Positone Hammerstein integral equations and applications. Communications on Pure and Applied Analysis, 2007, 6 (2) : 441-451. doi: 10.3934/cpaa.2007.6.441

[2]

Bhargav Kumar Kakumani, Suman Kumar Tumuluri. Asymptotic behavior of the solution of a diffusion equation with nonlocal boundary conditions. Discrete and Continuous Dynamical Systems - B, 2017, 22 (2) : 407-419. doi: 10.3934/dcdsb.2017019

[3]

G. Infante. Positive solutions of nonlocal boundary value problems with singularities. Conference Publications, 2009, 2009 (Special) : 377-384. doi: 10.3934/proc.2009.2009.377

[4]

John R. Graef, Lingju Kong, Qingkai Kong, Min Wang. Positive solutions of nonlocal fractional boundary value problems. Conference Publications, 2013, 2013 (special) : 283-290. doi: 10.3934/proc.2013.2013.283

[5]

Gabriella Di Blasio. Ultraparabolic equations with nonlocal delayed boundary conditions. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 4945-4965. doi: 10.3934/dcds.2013.33.4945

[6]

Gennaro Infante. Positive solutions of differential equations with nonlinear boundary conditions. Conference Publications, 2003, 2003 (Special) : 432-438. doi: 10.3934/proc.2003.2003.432

[7]

Qianqian Hou, Tai-Chia Lin, Zhi-An Wang. On a singularly perturbed semi-linear problem with Robin boundary conditions. Discrete and Continuous Dynamical Systems - B, 2021, 26 (1) : 401-414. doi: 10.3934/dcdsb.2020083

[8]

Mahamadi Warma. Semi linear parabolic equations with nonlinear general Wentzell boundary conditions. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5493-5506. doi: 10.3934/dcds.2013.33.5493

[9]

John R. Graef, Bo Yang. Positive solutions of a third order nonlocal boundary value problem. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 89-97. doi: 10.3934/dcdss.2008.1.89

[10]

Alexander Quaas, Andrei Rodríguez. Analysis of the attainment of boundary conditions for a nonlocal diffusive Hamilton-Jacobi equation. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 5221-5243. doi: 10.3934/dcds.2018231

[11]

Le Thi Phuong Ngoc, Nguyen Thanh Long. Existence and exponential decay for a nonlinear wave equation with nonlocal boundary conditions. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2001-2029. doi: 10.3934/cpaa.2013.12.2001

[12]

Boumediene Abdellaoui, Ahmed Attar, Abdelrazek Dieb, Ireneo Peral. Attainability of the fractional hardy constant with nonlocal mixed boundary conditions: Applications. Discrete and Continuous Dynamical Systems, 2018, 38 (12) : 5963-5991. doi: 10.3934/dcds.2018131

[13]

Kehan Shi, Ying Wen. Nonlocal biharmonic evolution equations with Dirichlet and Navier boundary conditions. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022089

[14]

Gennaro Infante. Eigenvalues and positive solutions of odes involving integral boundary conditions. Conference Publications, 2005, 2005 (Special) : 436-442. doi: 10.3934/proc.2005.2005.436

[15]

Dagny Butler, Eunkyung Ko, Eun Kyoung Lee, R. Shivaji. Positive radial solutions for elliptic equations on exterior domains with nonlinear boundary conditions. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2713-2731. doi: 10.3934/cpaa.2014.13.2713

[16]

Alberto Boscaggin, Francesca Colasuonno, Benedetta Noris. Positive radial solutions for the Minkowski-curvature equation with Neumann boundary conditions. Discrete and Continuous Dynamical Systems - S, 2020, 13 (7) : 1921-1933. doi: 10.3934/dcdss.2020150

[17]

Nicola Abatangelo, Serena Dipierro, Mouhamed Moustapha Fall, Sven Jarohs, Alberto Saldaña. Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1205-1235. doi: 10.3934/dcds.2019052

[18]

Abdelkader Boucherif. Positive Solutions of second order differential equations with integral boundary conditions. Conference Publications, 2007, 2007 (Special) : 155-159. doi: 10.3934/proc.2007.2007.155

[19]

Shin-Ichiro Ei, Toshio Ishimoto. Effect of boundary conditions on the dynamics of a pulse solution for reaction-diffusion systems. Networks and Heterogeneous Media, 2013, 8 (1) : 191-209. doi: 10.3934/nhm.2013.8.191

[20]

Minoo Kamrani. Numerical solution of partial differential equations with stochastic Neumann boundary conditions. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5337-5354. doi: 10.3934/dcdsb.2019061

2021 Impact Factor: 1.273

Metrics

  • PDF downloads (157)
  • HTML views (0)
  • Cited by (25)

Other articles
by authors

[Back to Top]