Name
Title | ||
|---|---|---|
Multiple Positive Solutions of Singular Nonlinear Sturm-Liouville Problems with Carathéodory Perturbed Term. |
Abstract | ||
|---|---|---|
By employing a well-known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth-order singular differential equation Lu = p(t) f(t,u(t),u "(t)) - g (t, u(t), u "(t)), 0 <t < 1, alpha(1)u(0) - beta(1)u'(0) = 0, gamma(1)u(1) + delta(1)u'(1) = 0, alpha(2)u "(0) - beta(2)u"'(0) = 0, gamma(2)u "(1) + delta(2)u"'(1) = 0, with alpha(i), beta(i), gamma(i), delta(i) >= 0 and beta(i)gamma(i) + alpha(i)gamma(i) + alpha(i)delta(i) > 0, i = 1, 2, where L denotes the linear operator Lu := (ru"') - qu ", r is an element of C-1([0, 1], (0, +infinity 8)), and q is an element of C([0, 1], [0, +8 infinity)). This equation is viewed as a perturbation of the fourth-order Sturm-Liouville problem, where the perturbed term g : (0, 1) x [0, +infinity) x (-infinity, +infinity) -> (-infinity, +infinity) only satisfies the global Caratheodory conditions, which implies that the perturbed effect of g on f is quite large so that the nonlinearity can tend to negative infinity at some singular points. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1155/2012/160891 | JOURNAL OF APPLIED MATHEMATICS |
Field | DocType | Volume |
Regular singular point,Differential equation,Extended real number line,Mathematical optimization,Sturm–Liouville theory,Nonlinear system,Mathematical analysis,Singular solution,Linear map,Fixed-point theorem,Mathematics | Journal | 2012 |
Issue | ISSN | Citations |
null | 1110-757X | 0 |
PageRank | References | Authors |
0.34 | 5 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuefeng Han | 1 | 16 | 1.87 |
| Xinguang Zhang | 2 | 163 | 23.65 |
| Lishan Liu | 3 | 188 | 35.41 |
| Yonghong Wu | 4 | 212 | 34.70 |