
Previous Article
Representation formula for the plane closed elastic curves
 PROC Home
 This Issue

Next Article
A note on optimal control problem for a hemivariational inequality modeling fluid flow
Existence and multiplicity of solutions in fourth order BVPs with unbounded nonlinearities
1.  Departamento de Matemática. Universidade de Évora, Centro de Investigação em Matemática e Aplicaçoes da U.E. (CIMAUE), Rua Romão Ramalho, 59. 7000671 Évora 
2.  College of the Bahamas, School of Mathematics, Physics and Technologies, Department of Mathematics, Oakes Field Campus, Nassau, Bahamas 
The arguments used apply lower and upper solutions technique and topological degree theory.
An application is made to a continuous model of the human spine, used in aircraft ejections, vehicle crash situations, and some forms of scoliosis.
References:
show all references
References:
[1] 
Xuewei Cui, Mei Yu. Nonexistence of positive solutions for a higher order fractional equation. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 13791387. doi: 10.3934/dcds.2019059 
[2] 
F. R. Pereira. Multiple solutions for a class of AmbrosettiProdi type problems for systems involving critical Sobolev exponents. Communications on Pure and Applied Analysis, 2008, 7 (2) : 355372. doi: 10.3934/cpaa.2008.7.355 
[3] 
Delia Schiera. Existence and nonexistence results for variational higher order elliptic systems. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 51455161. doi: 10.3934/dcds.2018227 
[4] 
Rubén Figueroa, Rodrigo López Pouso, Jorge Rodríguez–López. Existence and multiplicity results for secondorder discontinuous problems via nonordered lower and upper solutions. Discrete and Continuous Dynamical Systems  B, 2020, 25 (2) : 617633. doi: 10.3934/dcdsb.2019257 
[5] 
Imene Bendahou, Zied Khemiri, Fethi Mahmoudi. On spikes concentrating on lines for a Neumann superlinear AmbrosettiProdi type problem. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 23672391. doi: 10.3934/dcds.2020118 
[6] 
Elisa Sovrano. AmbrosettiProdi type result to a Neumann problem via a topological approach. Discrete and Continuous Dynamical Systems  S, 2018, 11 (2) : 345355. doi: 10.3934/dcdss.2018019 
[7] 
Yingshu Lü. Symmetry and nonexistence of solutions to an integral system. Communications on Pure and Applied Analysis, 2018, 17 (3) : 807821. doi: 10.3934/cpaa.2018041 
[8] 
Keisuke Matsuya, Tetsuji Tokihiro. Existence and nonexistence of global solutions for a discrete semilinear heat equation. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 209220. doi: 10.3934/dcds.2011.31.209 
[9] 
J. F. Toland. Nonexistence of global energy minimisers in Stokes waves problems. Discrete and Continuous Dynamical Systems, 2014, 34 (8) : 32113217. doi: 10.3934/dcds.2014.34.3211 
[10] 
Ran Zhuo, Wenxiong Chen, Xuewei Cui, Zixia Yuan. Symmetry and nonexistence of solutions for a nonlinear system involving the fractional Laplacian. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 11251141. doi: 10.3934/dcds.2016.36.1125 
[11] 
ShuYu Hsu. Nonexistence and behaviour at infinity of solutions of some elliptic equations. Discrete and Continuous Dynamical Systems, 2004, 10 (3) : 769786. doi: 10.3934/dcds.2004.10.769 
[12] 
Fuqin Sun, Mingxin Wang. Nonexistence of global solutions for nonlinear strongly damped hyperbolic systems. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 949958. doi: 10.3934/dcds.2005.12.949 
[13] 
Eun Bee Choi, YunHo Kim. Existence of nontrivial solutions for equations of $p(x)$Laplace type without Ambrosetti and Rabinowitz condition. Conference Publications, 2015, 2015 (special) : 276286. doi: 10.3934/proc.2015.0276 
[14] 
Luis Barreira, Davor Dragičević, Claudia Valls. From onesided dichotomies to twosided dichotomies. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 28172844. doi: 10.3934/dcds.2015.35.2817 
[15] 
WolfJüergen Beyn, Janosch Rieger. The implicit Euler scheme for onesided Lipschitz differential inclusions. Discrete and Continuous Dynamical Systems  B, 2010, 14 (2) : 409428. doi: 10.3934/dcdsb.2010.14.409 
[16] 
Yulong Li, Aleksey S. Telyakovskiy, Emine Çelik. Analysis of onesided 1D fractional diffusion operator. Communications on Pure and Applied Analysis, 2022, 21 (5) : 16731690. doi: 10.3934/cpaa.2022039 
[17] 
Lauren M. M. Bonaldo, Elard J. Hurtado, Olímpio H. Miyagaki. Multiplicity results for elliptic problems involving nonlocal integrodifferential operators without AmbrosettiRabinowitz condition. Discrete and Continuous Dynamical Systems, 2022, 42 (7) : 33293353. doi: 10.3934/dcds.2022017 
[18] 
Jitsuro Sugie, Tadayuki Hara. Existence and nonexistence of homoclinic trajectories of the Liénard system. Discrete and Continuous Dynamical Systems, 1996, 2 (2) : 237254. doi: 10.3934/dcds.1996.2.237 
[19] 
Elias M. Guio, Ricardo Sa Earp. Existence and nonexistence for a mean curvature equation in hyperbolic space. Communications on Pure and Applied Analysis, 2005, 4 (3) : 549568. doi: 10.3934/cpaa.2005.4.549 
[20] 
Jiafeng Liao, Peng Zhang, Jiu Liu, Chunlei Tang. Existence and multiplicity of positive solutions for a class of Kirchhoff type problems at resonance. Discrete and Continuous Dynamical Systems  S, 2016, 9 (6) : 19591974. doi: 10.3934/dcdss.2016080 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]