Existence of one-signed solutions of nonlinear four-point boundary value problems

Ruyun Ma; Ruipeng Chen

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 3, page 593-612
  • ISSN: 0011-4642

Abstract

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In this paper, we are concerned with the existence of one-signed solutions of four-point boundary value problems - u ' ' + M u = r g ( t ) f ( u ) , u ( 0 ) = u ( ε ) , u ( 1 ) = u ( 1 - ε ) and u ' ' + M u = r g ( t ) f ( u ) , u ( 0 ) = u ( ε ) , u ( 1 ) = u ( 1 - ε ) , where ε ∈ ( 0 , 1 / 2 ) , M ∈ ( 0 , ∞ ) is a constant and r > 0 is a parameter, g ∈ C ( [ 0 , 1 ] , ( 0 , + ∞ ) ) , f ∈ C ( ℝ , ℝ ) with s f ( s ) > 0 for s ≠ 0 . The proof of the main results is based upon bifurcation techniques.

How to cite

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Ma, Ruyun, and Chen, Ruipeng. "Existence of one-signed solutions of nonlinear four-point boundary value problems." Czechoslovak Mathematical Journal 62.3 (2012): 593-612. <http://eudml.org/doc/247221>.

@article{Ma2012,
abstract = {In this paper, we are concerned with the existence of one-signed solutions of four-point boundary value problems \[ -u^\{\prime \prime \}+Mu=rg(t)f(u), \quad u(0)=u(\varepsilon ),\quad u(1)=u(1-\varepsilon ) \] and \[ u^\{\prime \prime \}+Mu=rg(t)f(u), \quad u(0)=u(\varepsilon ),\quad u(1)=u(1-\varepsilon ), \] where $\varepsilon \in (0,\{1\}/\{2\})$, $M\in (0,\infty )$ is a constant and $r>0$ is a parameter, $g\in C([0,1],(0,+\infty ))$, $f\in C(\mathbb \{R\},\mathbb \{R\})$ with $sf(s)>0$ for $s\ne 0$. The proof of the main results is based upon bifurcation techniques.},
author = {Ma, Ruyun, Chen, Ruipeng},
journal = {Czechoslovak Mathematical Journal},
keywords = {four-point boundary value problem; one-signed solution; bifurcation method; four-point boundary value problem; one-signed solution; positive solution; negative solution; bifurcation method},
language = {eng},
number = {3},
pages = {593-612},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of one-signed solutions of nonlinear four-point boundary value problems},
url = {http://eudml.org/doc/247221},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Ma, Ruyun
AU - Chen, Ruipeng
TI - Existence of one-signed solutions of nonlinear four-point boundary value problems
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 3
SP - 593
EP - 612
AB - In this paper, we are concerned with the existence of one-signed solutions of four-point boundary value problems \[ -u^{\prime \prime }+Mu=rg(t)f(u), \quad u(0)=u(\varepsilon ),\quad u(1)=u(1-\varepsilon ) \] and \[ u^{\prime \prime }+Mu=rg(t)f(u), \quad u(0)=u(\varepsilon ),\quad u(1)=u(1-\varepsilon ), \] where $\varepsilon \in (0,{1}/{2})$, $M\in (0,\infty )$ is a constant and $r>0$ is a parameter, $g\in C([0,1],(0,+\infty ))$, $f\in C(\mathbb {R},\mathbb {R})$ with $sf(s)>0$ for $s\ne 0$. The proof of the main results is based upon bifurcation techniques.
LA - eng
KW - four-point boundary value problem; one-signed solution; bifurcation method; four-point boundary value problem; one-signed solution; positive solution; negative solution; bifurcation method
UR - http://eudml.org/doc/247221
ER -

References

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