Singular Dirichlet boundary value problems. II: Resonance case

Donal O'Regan

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 2, page 269-289
  • ISSN: 0011-4642

Abstract

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Existence results are established for the resonant problem y ' ' + λ m a y = f ( t , y ) a.e. on [ 0 , 1 ] with y satisfying Dirichlet boundary conditions. The problem is singular since f is a Carathéodory function, a ∈ L l o c 1 ( 0 , 1 ) with a > 0 a.e. on [ 0 , 1 ] and ∫ 0 1 x ( 1 - x ) a ( x ) d x < ∞ .

How to cite

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O'Regan, Donal. "Singular Dirichlet boundary value problems. II: Resonance case." Czechoslovak Mathematical Journal 48.2 (1998): 269-289. <http://eudml.org/doc/30418>.

@article{ORegan1998,
abstract = {Existence results are established for the resonant problem $y^\{\prime \prime \}+\lambda _m \,a\,y=f(t,y)$ a.e. on $[0,1]$ with $y$ satisfying Dirichlet boundary conditions. The problem is singular since $f$ is a Carathéodory function, $a\in L_\{\{\mathrm \{l\}oc\}\}^1(0,1)$ with $a>0$ a.e. on $[0,1]$ and $\int ^1_0 x(1-x)a(x)\,\mathrm \{d\}x <\infty $.},
author = {O'Regan, Donal},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlinear boundary value problem; singular problem; second-order nonlinear differential equation; Dirichlet problem; resonance case},
language = {eng},
number = {2},
pages = {269-289},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Singular Dirichlet boundary value problems. II: Resonance case},
url = {http://eudml.org/doc/30418},
volume = {48},
year = {1998},
}

TY - JOUR
AU - O'Regan, Donal
TI - Singular Dirichlet boundary value problems. II: Resonance case
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 2
SP - 269
EP - 289
AB - Existence results are established for the resonant problem $y^{\prime \prime }+\lambda _m \,a\,y=f(t,y)$ a.e. on $[0,1]$ with $y$ satisfying Dirichlet boundary conditions. The problem is singular since $f$ is a Carathéodory function, $a\in L_{{\mathrm {l}oc}}^1(0,1)$ with $a>0$ a.e. on $[0,1]$ and $\int ^1_0 x(1-x)a(x)\,\mathrm {d}x <\infty $.
LA - eng
KW - nonlinear boundary value problem; singular problem; second-order nonlinear differential equation; Dirichlet problem; resonance case
UR - http://eudml.org/doc/30418
ER -

References

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  8. 10.1216/RMJ-1982-12-4-643, Rocky M.J. Math. 112 (1982), 643–654. (1982) DOI10.1216/RMJ-1982-12-4-643
  9. Linear differential operators, Part II, Ungar Publ. Co., London, 1968. (1968) Zbl0227.34020MR0262880
  10. Theory of singular boundary value problems, World Scientific Press, Singapore, 1994. (1994) 
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  12. 10.1016/S0362-546X(96)00026-0, Nonlinear Analysis 29 (1997), 221–245. (1997) MR1446226DOI10.1016/S0362-546X(96)00026-0

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