• Previous Article
    Concentrating phenomena in some elliptic Neumann problem: Asymptotic behavior of solutions
  • CPAA Home
  • This Issue
  • Next Article
    Sign-changing multi-peak solutions for nonlinear Schrödinger equations with critical frequency
July  2008, 7(4): 905-923. doi: 10.3934/cpaa.2008.7.905

On the existence of nodal solutions for singular one-dimensional $\varphi$-Laplacian problem with asymptotic condition

1. 

Department of Mathematics, Pusan National University, Pusan 609-735, South Korea

Received  July 2007 Revised  February 2008 Published  April 2008

We obtain the existence results of nodal solutions for singular one-dimensional $\varphi$-Laplacian problem with asymptotic condition:

$\varphi (u'(t))' + \lambda h(t) f (u(t)) = 0,\ \ $ a.e. $\ t \in (0,1), \qquad\qquad\qquad\qquad\qquad $ $(\Phi_\lambda)$

$u(0) = 0=u(1),$

where $\varphi : \mathbb R \to \mathbb R$ is an odd increasing homeomorphism, $\lambda$ a positive parameter and $h \in L^1(0,1)$ a nonnegative measurable function on $(0,1)$ which may be singular at $t = 0$ and/or $t = 1,$ and $f \in C(\mathbb R, \mathbb R)$ and is odd.

Citation: Inbo Sim. On the existence of nodal solutions for singular one-dimensional $\varphi$-Laplacian problem with asymptotic condition. Communications on Pure & Applied Analysis, 2008, 7 (4) : 905-923. doi: 10.3934/cpaa.2008.7.905
[1]

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

[2]

Shao-Yuan Huang. Global bifurcation and exact multiplicity of positive solutions for the one-dimensional Minkowski-curvature problem with sign-changing nonlinearity. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3267-3284. doi: 10.3934/cpaa.2019147

[3]

Haibo Cui, Junpei Gao, Lei Yao. Asymptotic behavior of the one-dimensional compressible micropolar fluid model. Electronic Research Archive, 2021, 29 (2) : 2063-2075. doi: 10.3934/era.2020105

[4]

Zhi-An Wang, Kun Zhao. Global dynamics and diffusion limit of a one-dimensional repulsive chemotaxis model. Communications on Pure & Applied Analysis, 2013, 12 (6) : 3027-3046. doi: 10.3934/cpaa.2013.12.3027

[5]

Yuxi Hu, Na Wang. On global solutions in one-dimensional thermoelasticity with second sound in the half line. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1671-1683. doi: 10.3934/cpaa.2015.14.1671

[6]

Shao-Yuan Huang. Bifurcation diagrams of positive solutions for one-dimensional Minkowski-curvature problem and its applications. Discrete & Continuous Dynamical Systems, 2019, 39 (6) : 3443-3462. doi: 10.3934/dcds.2019142

[7]

Yanan Li, Alexandre N. Carvalho, Tito L. M. Luna, Estefani M. Moreira. A non-autonomous bifurcation problem for a non-local scalar one-dimensional parabolic equation. Communications on Pure & Applied Analysis, 2020, 19 (11) : 5181-5196. doi: 10.3934/cpaa.2020232

[8]

Julián López-Gómez, Marcela Molina-Meyer, Andrea Tellini. Intricate bifurcation diagrams for a class of one-dimensional superlinear indefinite problems of interest in population dynamics. Conference Publications, 2013, 2013 (special) : 515-524. doi: 10.3934/proc.2013.2013.515

[9]

Shao-Yuan Huang. Exact multiplicity and bifurcation curves of positive solutions of a one-dimensional Minkowski-curvature problem and its application. Communications on Pure & Applied Analysis, 2018, 17 (3) : 1271-1294. doi: 10.3934/cpaa.2018061

[10]

Yu-Hao Liang, Shin-Hwa Wang. Classification and evolution of bifurcation curves for a one-dimensional Dirichlet-Neumann problem with a specific cubic nonlinearity. Discrete & Continuous Dynamical Systems, 2020, 40 (2) : 1075-1105. doi: 10.3934/dcds.2020071

[11]

Akane Kawaharada. Singular function emerging from one-dimensional elementary cellular automaton Rule 150. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021125

[12]

Umberto Biccari. Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential. Mathematical Control & Related Fields, 2019, 9 (1) : 191-219. doi: 10.3934/mcrf.2019011

[13]

Lili Fan, Lizhi Ruan, Wei Xiang. Asymptotic stability of viscous contact wave for the inflow problem of the one-dimensional radiative Euler equations. Discrete & Continuous Dynamical Systems, 2021, 41 (4) : 1971-1999. doi: 10.3934/dcds.2020349

[14]

Jie Jiang, Boling Guo. Asymptotic behavior of solutions to a one-dimensional full model for phase transitions with microscopic movements. Discrete & Continuous Dynamical Systems, 2012, 32 (1) : 167-190. doi: 10.3934/dcds.2012.32.167

[15]

Ken Shirakawa. Asymptotic stability for dynamical systems associated with the one-dimensional Frémond model of shape memory alloys. Conference Publications, 2003, 2003 (Special) : 798-808. doi: 10.3934/proc.2003.2003.798

[16]

François James, Nicolas Vauchelet. One-dimensional aggregation equation after blow up: Existence, uniqueness and numerical simulation. Networks & Heterogeneous Media, 2016, 11 (1) : 163-180. doi: 10.3934/nhm.2016.11.163

[17]

Franco Obersnel, Pierpaolo Omari. Existence, regularity and boundary behaviour of bounded variation solutions of a one-dimensional capillarity equation. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 305-320. doi: 10.3934/dcds.2013.33.305

[18]

Denis Mercier, Serge Nicaise. Existence results for general systems of differential equations on one-dimensional networks and prewavelets approximation. Discrete & Continuous Dynamical Systems, 1998, 4 (2) : 273-300. doi: 10.3934/dcds.1998.4.273

[19]

Colette Guillopé, Samer Israwi, Raafat Talhouk. Large-time existence for one-dimensional Green-Naghdi equations with vorticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (8) : 2947-2974. doi: 10.3934/dcdss.2021040

[20]

Eduardo Liz. Local stability implies global stability in some one-dimensional discrete single-species models. Discrete & Continuous Dynamical Systems - B, 2007, 7 (1) : 191-199. doi: 10.3934/dcdsb.2007.7.191

2020 Impact Factor: 1.916

Metrics

  • PDF downloads (44)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]