-
Previous Article
A stability estimate for fluid structure interaction problem with non-linear beam
- PROC Home
- This Issue
-
Next Article
Intelligent traffic control on internet-like topologies - integration of graph principles to the classic Runge--Kutta method
Existence and nonexistence of positive solutions for a nonlinear fractional boundary value problem
1. | Department of Mathematics & Statistics, University of Arkansas at Little Rock, Little Rock, AR 72204, United States |
$\D_0^\alpha + u(t) + f(t, u(t)) = 0,$ $t \in (0, \tau),$
$I^\gamma u(0^+) = 0,$ $I^\beta u(\tau) = 0,$
where $1 - \alpha < \gamma \leq 2 - \alpha,$ $2 - \alpha < \beta < 0$, $\D_(0+)^\alpha$ is the Riemann-Liouville differential operator of order $\alpha $, and $f \in C([0,T] \times \mathbb{R})$ is nonnegative, has a positive solution. We also present a nonexistence result.
[1] |
Editorial Office. WITHDRAWN: Fractional diffusion equation described by the Atangana-Baleanu fractional derivative and its approximate solution. Discrete and Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2020173 |
[2] |
Kaouther Bouchama, Yacine Arioua, Abdelkrim Merzougui. The Numerical Solution of the space-time fractional diffusion equation involving the Caputo-Katugampola fractional derivative. Numerical Algebra, Control and Optimization, 2022, 12 (3) : 621-636. doi: 10.3934/naco.2021026 |
[3] |
Changpin Li, Zhiqiang Li. Asymptotic behaviors of solution to partial differential equation with Caputo–Hadamard derivative and fractional Laplacian: Hyperbolic case. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3659-3683. doi: 10.3934/dcdss.2021023 |
[4] |
Xudong Shang, Jihui Zhang. Multiplicity and concentration of positive solutions for fractional nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2239-2259. doi: 10.3934/cpaa.2018107 |
[5] |
Xudong Shang, Jihui Zhang. Multi-peak positive solutions for a fractional nonlinear elliptic equation. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 3183-3201. doi: 10.3934/dcds.2015.35.3183 |
[6] |
Qi Li, Kefan Pan, Shuangjie Peng. Positive solutions to a nonlinear fractional equation with an external source term. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022068 |
[7] |
Christina A. Hollon, Jeffrey T. Neugebauer. Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition. Conference Publications, 2015, 2015 (special) : 615-620. doi: 10.3934/proc.2015.0615 |
[8] |
Weiming Liu, Lu Gan. Multi-bump positive solutions of a fractional nonlinear Schrödinger equation in $\mathbb{R}^N$. Communications on Pure and Applied Analysis, 2016, 15 (2) : 413-428. doi: 10.3934/cpaa.2016.15.413 |
[9] |
Tran Bao Ngoc, Nguyen Huy Tuan, R. Sakthivel, Donal O'Regan. Analysis of nonlinear fractional diffusion equations with a Riemann-liouville derivative. Evolution Equations and Control Theory, 2022, 11 (2) : 439-455. doi: 10.3934/eect.2021007 |
[10] |
Út V. Lê. Regularity of the solution of a nonlinear wave equation. Communications on Pure and Applied Analysis, 2010, 9 (4) : 1099-1115. doi: 10.3934/cpaa.2010.9.1099 |
[11] |
Daria Bugajewska, Mirosława Zima. On positive solutions of nonlinear fractional differential equations. Conference Publications, 2003, 2003 (Special) : 141-146. doi: 10.3934/proc.2003.2003.141 |
[12] |
Alain Miranville, Costică Moroşanu. Analysis of an iterative scheme of fractional steps type associated to the nonlinear phase-field equation with non-homogeneous dynamic boundary conditions. Discrete and Continuous Dynamical Systems - S, 2016, 9 (2) : 537-556. doi: 10.3934/dcdss.2016011 |
[13] |
Carl. T. Kelley, Liqun Qi, Xiaojiao Tong, Hongxia Yin. Finding a stable solution of a system of nonlinear equations arising from dynamic systems. Journal of Industrial and Management Optimization, 2011, 7 (2) : 497-521. doi: 10.3934/jimo.2011.7.497 |
[14] |
Chun Wang, Tian-Zhou Xu. Stability of the nonlinear fractional differential equations with the right-sided Riemann-Liouville fractional derivative. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 505-521. doi: 10.3934/dcdss.2017025 |
[15] |
Razvan Mosincat, Haewon Yoon. Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 47-80. doi: 10.3934/dcds.2020003 |
[16] |
Meina Gao, Jianjun Liu. Quasi-periodic solutions for derivative nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 2101-2123. doi: 10.3934/dcds.2012.32.2101 |
[17] |
Nakao Hayashi, Elena I. Kaikina, Pavel I. Naumkin. Large time behavior of solutions to the generalized derivative nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 1999, 5 (1) : 93-106. doi: 10.3934/dcds.1999.5.93 |
[18] |
Hiroyuki Hirayama, Mamoru Okamoto. Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 6943-6974. doi: 10.3934/dcds.2016102 |
[19] |
Kazumasa Fujiwara, Tohru Ozawa. On the lifespan of strong solutions to the periodic derivative nonlinear Schrödinger equation. Evolution Equations and Control Theory, 2018, 7 (2) : 275-280. doi: 10.3934/eect.2018013 |
[20] |
Nakao Hayashi, Pavel I. Naumkin. Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation revisited. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 383-400. doi: 10.3934/dcds.1997.3.383 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]