Geodesic
Existence of one-signed solutions of nonlinear four-point boundary value problems
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 3, pp. 593-612

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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 $\varepsilon \in (0,{1}/{2})$, $M\in (0,\infty )$ 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 $s\neq 0$. The proof of the main results is based upon bifurcation techniques.
DOI : 10.1007/s10587-012-0052-3
Classification : 34B10, 34B15, 34B18, 34C23
Keywords: four-point boundary value problem; one-signed solution; bifurcation method 
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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

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