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

Ma, Ruyun; Chen, Ruipeng

doi:10.1007/s10587-012-0052-3

Geodesic

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

Ma, Ruyun ; Chen, Ruipeng

Czechoslovak Mathematical Journal, Tome 62 (2012) no. 3, pp. 593-612.

Voir la notice de l'article dans Czech Digital Mathematics Library

Résumé

In this paper, we are concerned with the existence of one-signed solutions of four-point boundary value problems $$ -u''+Mu=rg(t)f(u), \quad u(0)=u(\varepsilon ),\quad u(1)=u(1-\varepsilon ) $$ and $$ u''+Mu=rg(t)f(u), \quad u(0)=u(\varepsilon ),\quad u(1)=u(1-\varepsilon ), $$ where

ε \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 (R, R)

with

s f (s) > 0

for

s \neq 0

. The proof of the main results is based upon bifurcation techniques.

MR Zbl

DOI : 10.1007/s10587-012-0052-3

Classification : 34B10, 34B15, 34B18, 34C23
Mots-clés : four-point boundary value problem; one-signed solution; bifurcation method

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     title = {Existence of one-signed solutions of nonlinear four-point boundary value problems},
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Ma, Ruyun; Chen, Ruipeng. Existence of one-signed solutions of nonlinear four-point boundary value problems. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 3, pp. 593-612. doi : 10.1007/s10587-012-0052-3. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0052-3/

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