Bifurcation from intervals for Sturm-Liouville problems and its applications
We study the unilateral global bifurcation for the nonlinear Sturm-Liouville problem $$\displaylines{ -(pu')'+qu=\lambda au+af(x,u,u',\lambda)+g(x,u,u',\lambda)\quad x\in(0,1),\cr b_0u(0)+c_0u'(0)=0,\quad b_1u(1)+c_1u'(1)=0, }$$ where $a\in C([0, 1], [0,+\infty))$...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/03/abstr.html |
| Summary: | We study the unilateral global bifurcation for the nonlinear
Sturm-Liouville problem
$$\displaylines{
-(pu')'+qu=\lambda au+af(x,u,u',\lambda)+g(x,u,u',\lambda)\quad x\in(0,1),\cr
b_0u(0)+c_0u'(0)=0,\quad b_1u(1)+c_1u'(1)=0,
}$$
where $a\in C([0, 1], [0,+\infty))$ and $a(x)\not\equiv 0$ on any subinterval
of $[0, 1]$, $f,g\in C([0,1]\times\mathbb{R}^3,\mathbb{R})$ and f is
not necessarily differentiable at the origin or infinity with respect to u.
Some applications are given to nonlinear second-order two-point boundary-value
problems. This article is a continuation of [8]. |
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| ISSN: | 1072-6691 |