Differential equations at resonance

Donal O'Regan

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 4, page 673-694
  • ISSN: 0010-2628

Abstract

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New existence results are presented for the two point singular “resonant” boundary value problem 1 p ( p y ' ) ' + r y + λ m q y = f ( t , y , p y ' ) a.eȯn [ 0 , 1 ] with y satisfying Sturm Liouville or Periodic boundary conditions. Here λ m is the ( m + 1 ) s t eigenvalue of 1 p q [ ( p u ' ) ' + r p u ] + λ u = 0 a.eȯn [ 0 , 1 ] with u satisfying Sturm Liouville or Periodic boundary data.

How to cite

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O'Regan, Donal. "Differential equations at resonance." Commentationes Mathematicae Universitatis Carolinae 36.4 (1995): 673-694. <http://eudml.org/doc/247735>.

@article{ORegan1995,
abstract = {New existence results are presented for the two point singular “resonant” boundary value problem $\frac\{1\}\{p\}(py^\{\prime \})^\{\prime \}+r y+\lambda _m qy=f(t,y,py^\{\prime \})$ a.eȯn $[0,1]$ with $y$ satisfying Sturm Liouville or Periodic boundary conditions. Here $\lambda _m$ is the $(m+1)^\{st\}$ eigenvalue of $\frac\{1\}\{pq\} [(pu^\{\prime \})^\{\prime \} +rpu] +\lambda u=0$ a.eȯn $[0,1]$ with $u$ satisfying Sturm Liouville or Periodic boundary data.},
author = {O'Regan, Donal},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {boundary value problems; resonance; existence; boundary value problems; eigenvalue; resonance; existence},
language = {eng},
number = {4},
pages = {673-694},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Differential equations at resonance},
url = {http://eudml.org/doc/247735},
volume = {36},
year = {1995},
}

TY - JOUR
AU - O'Regan, Donal
TI - Differential equations at resonance
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 4
SP - 673
EP - 694
AB - New existence results are presented for the two point singular “resonant” boundary value problem $\frac{1}{p}(py^{\prime })^{\prime }+r y+\lambda _m qy=f(t,y,py^{\prime })$ a.eȯn $[0,1]$ with $y$ satisfying Sturm Liouville or Periodic boundary conditions. Here $\lambda _m$ is the $(m+1)^{st}$ eigenvalue of $\frac{1}{pq} [(pu^{\prime })^{\prime } +rpu] +\lambda u=0$ a.eȯn $[0,1]$ with $u$ satisfying Sturm Liouville or Periodic boundary data.
LA - eng
KW - boundary value problems; resonance; existence; boundary value problems; eigenvalue; resonance; existence
UR - http://eudml.org/doc/247735
ER -

References

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