-
Previous Article
Gevrey-smoothness of invariant tori for analytic reversible systems under Rüssmann's non-degeneracy condition
- DCDS Home
- This Issue
-
Next Article
Hölder forms and integrability of invariant distributions
Existence and monotonicity property of minimizers of a nonconvex variational problem with a second-order Lagrangian
| 1. | College of Mathematics, Jilin University, Changchun 130012 |
| 2. | Department of Mathematics, Jilin University, Changchun 130023 |
Minimize $\quad \int_a^bL(x,u(x),u'(x),u''(x))dx,\quad u\in\Omega$
with a second-order Lagrangian is considered. In absence of any smoothness or convexity condition on $L$, we present an existence theorem by means of the integro-extremal technique. We also discuss the monotonicity property of the minimizers. An application to the extended Fisher-Kolmogorov model is included.
| [1] |
Leonardo Colombo, David Martín de Diego. Second-order variational problems on Lie groupoids and optimal control applications. Discrete & Continuous Dynamical Systems, 2016, 36 (11) : 6023-6064. doi: 10.3934/dcds.2016064 |
| [2] |
Leonardo Colombo. Second-order constrained variational problems on Lie algebroids: Applications to Optimal Control. Journal of Geometric Mechanics, 2017, 9 (1) : 1-45. doi: 10.3934/jgm.2017001 |
| [3] |
Rubén Figueroa, Rodrigo López Pouso, Jorge Rodríguez–López. Existence and multiplicity results for second-order discontinuous problems via non-ordered lower and upper solutions. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 617-633. doi: 10.3934/dcdsb.2019257 |
| [4] |
Johnny Henderson, Rodica Luca. Existence of positive solutions for a system of nonlinear second-order integral boundary value problems. Conference Publications, 2015, 2015 (special) : 596-604. doi: 10.3934/proc.2015.0596 |
| [5] |
Cheng Wang, Jian-Guo Liu. Positivity property of second-order flux-splitting schemes for the compressible Euler equations. Discrete & Continuous Dynamical Systems - B, 2003, 3 (2) : 201-228. doi: 10.3934/dcdsb.2003.3.201 |
| [6] |
Nobusumi Sagara. Recursive variational problems in nonreflexive Banach spaces with an infinite horizon: An existence result. Discrete & Continuous Dynamical Systems - S, 2018, 11 (6) : 1219-1232. doi: 10.3934/dcdss.2018069 |
| [7] |
Ziye Shi, Qingwei Jin. Second order optimality conditions and reformulations for nonconvex quadratically constrained quadratic programming problems. Journal of Industrial & Management Optimization, 2014, 10 (3) : 871-882. doi: 10.3934/jimo.2014.10.871 |
| [8] |
Christos Gavriel, Richard Vinter. Regularity of minimizers for second order variational problems in one independent variable. Discrete & Continuous Dynamical Systems, 2011, 29 (2) : 547-557. doi: 10.3934/dcds.2011.29.547 |
| [9] |
Dong-Lun Wu, Chun-Lei Tang, Xing-Ping Wu. Existence and nonuniqueness of homoclinic solutions for second-order Hamiltonian systems with mixed nonlinearities. Communications on Pure & Applied Analysis, 2016, 15 (1) : 57-72. doi: 10.3934/cpaa.2016.15.57 |
| [10] |
Kaifang Liu, Lunji Song, Shan Zhao. A new over-penalized weak galerkin method. Part Ⅰ: Second-order elliptic problems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2411-2428. doi: 10.3934/dcdsb.2020184 |
| [11] |
Doyoon Kim, Seungjin Ryu. The weak maximum principle for second-order elliptic and parabolic conormal derivative problems. Communications on Pure & Applied Analysis, 2020, 19 (1) : 493-510. doi: 10.3934/cpaa.2020024 |
| [12] |
Shasha Hu, Yihong Xu, Yuhan Zhang. Second-Order characterizations for set-valued equilibrium problems with variable ordering structures. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020164 |
| [13] |
Yanhong Yuan, Hongwei Zhang, Liwei Zhang. A smoothing Newton method for generalized Nash equilibrium problems with second-order cone constraints. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 1-18. doi: 10.3934/naco.2012.2.1 |
| [14] |
Hongwei Lou. Second-order necessary/sufficient conditions for optimal control problems in the absence of linear structure. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1445-1464. doi: 10.3934/dcdsb.2010.14.1445 |
| [15] |
Guanrong Li, Yanping Chen, Yunqing Huang. A hybridized weak Galerkin finite element scheme for general second-order elliptic problems. Electronic Research Archive, 2020, 28 (2) : 821-836. doi: 10.3934/era.2020042 |
| [16] |
Doria Affane, Mustapha Fateh Yarou. Well-posed control problems related to second-order differential inclusions. Evolution Equations & Control Theory, 2021 doi: 10.3934/eect.2021042 |
| [17] |
José F. Cariñena, Javier de Lucas Araujo. Superposition rules and second-order Riccati equations. Journal of Geometric Mechanics, 2011, 3 (1) : 1-22. doi: 10.3934/jgm.2011.3.1 |
| [18] |
Eugenii Shustin, Emilia Fridman, Leonid Fridman. Oscillations in a second-order discontinuous system with delay. Discrete & Continuous Dynamical Systems, 2003, 9 (2) : 339-358. doi: 10.3934/dcds.2003.9.339 |
| [19] |
Daniel Franco, Donal O'Regan. Existence of solutions to second order problems with nonlinear boundary conditions. Conference Publications, 2003, 2003 (Special) : 273-280. doi: 10.3934/proc.2003.2003.273 |
| [20] |
Mário Jorge Dias Carneiro, Alexandre Rocha. A generic property of exact magnetic Lagrangians. Discrete & Continuous Dynamical Systems, 2012, 32 (12) : 4183-4194. doi: 10.3934/dcds.2012.32.4183 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]