Singular Dirichlet problem for ordinary differential equations with φ -Laplacian

Vladimír Polášek; Irena Rachůnková

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 4, page 409-425
  • ISSN: 0862-7959

Abstract

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We provide sufficient conditions for solvability of a singular Dirichlet boundary value problem with - L a p l a c i a n . ((u)) = f(t, u, u), u(0) = A, u(T) = B, . w h e r e is an increasing homeomorphism, ( ℝ ) = ℝ , ( 0 ) = 0 , f satisfies the Carathéodory conditions on each set [ a , b ] × ℝ 2 with [ a , b ] ⊂ ( 0 , T ) and f is not integrable on [ 0 , T ] for some fixed values of its phase variables. We prove the existence of a solution which has continuous first derivative on [ 0 , T ] .

How to cite

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Polášek, Vladimír, and Rachůnková, Irena. "Singular Dirichlet problem for ordinary differential equations with $\phi $-Laplacian." Mathematica Bohemica 130.4 (2005): 409-425. <http://eudml.org/doc/249593>.

@article{Polášek2005,
abstract = {We provide sufficient conditions for solvability of a singular Dirichlet boundary value problem with \[-Laplacian \] . ((u)) = f(t, u, u), u(0) = A, u(T) = B, . \[ where \] is an increasing homeomorphism, $(\mathbb \{R\})=\mathbb \{R\}$, $(0)=0$, $f$ satisfies the Carathéodory conditions on each set $[a, b]\times \mathbb \{R\}^\{2\}$ with $[a, b]\subset (0, T)$ and $f$ is not integrable on $[0, T]$ for some fixed values of its phase variables. We prove the existence of a solution which has continuous first derivative on $[0, T]$.},
author = {Polášek, Vladimír, Rachůnková, Irena},
journal = {Mathematica Bohemica},
keywords = {existence of smooth solution; lower function; upper function},
language = {eng},
number = {4},
pages = {409-425},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Singular Dirichlet problem for ordinary differential equations with $\phi $-Laplacian},
url = {http://eudml.org/doc/249593},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Polášek, Vladimír
AU - Rachůnková, Irena
TI - Singular Dirichlet problem for ordinary differential equations with $\phi $-Laplacian
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 4
SP - 409
EP - 425
AB - We provide sufficient conditions for solvability of a singular Dirichlet boundary value problem with \[-Laplacian \] . ((u)) = f(t, u, u), u(0) = A, u(T) = B, . \[ where \] is an increasing homeomorphism, $(\mathbb {R})=\mathbb {R}$, $(0)=0$, $f$ satisfies the Carathéodory conditions on each set $[a, b]\times \mathbb {R}^{2}$ with $[a, b]\subset (0, T)$ and $f$ is not integrable on $[0, T]$ for some fixed values of its phase variables. We prove the existence of a solution which has continuous first derivative on $[0, T]$.
LA - eng
KW - existence of smooth solution; lower function; upper function
UR - http://eudml.org/doc/249593
ER -

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