| Title:
|
On some properties of the solution of the differential equation $u''+\frac{2u'}{r}=u-u^3$ (English) |
| Author:
|
Šeda, Valter |
| Author:
|
Pekár, Ján |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1990 |
| Pages:
|
315-336 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper it is shown that each solution $u(r,\alpha)$ ot the initial value problem (2), (3) has a finite limit for $r\rightarrow \infty$, and an asymptotic formula for the nontrivial solution $u(r,\alpha)$ tending to 0 is given. Further, the existence of such a solutions is established by examining the number of zeros of two different solutions $u(r,\bar{\alpha})$, $u(r,\hat{\alpha})$. (English) |
| Keyword:
|
spherically symmetric solution |
| Keyword:
|
trajectory of the solution |
| Keyword:
|
со-limit point of the trajectory |
| Keyword:
|
asymptotic formula |
| Keyword:
|
antitone and contractive operator |
| Keyword:
|
zero of the solution |
| Keyword:
|
Klein-Gordon equation |
| Keyword:
|
global behavior |
| MSC:
|
34A12 |
| MSC:
|
34C10 |
| MSC:
|
34D05 |
| MSC:
|
34E99 |
| MSC:
|
35Q40 |
| idZBL:
|
Zbl 0719.34058 |
| idMR:
|
MR1065005 |
| DOI:
|
10.21136/AM.1990.104413 |
| . |
| Date available:
|
2008-05-20T18:39:37Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104413 |
| . |
| Reference:
|
[1] Ch. V. Coffman: Uniqueness of the ground state solution for $\Delta u - u +u^3 = 0$ and a variational characterization of other solutions.Arch. Rational Mech. Anal. 46 (1972), 81 - 95. MR 0333489, 10.1007/BF00250684 |
| Reference:
|
[2] L. Erbe K. Schmitt: On radial solutions of some semilinear elliptic equations.Differential and Integral Equations, Vol. 1 (1988), 71 - 78. MR 0920490 |
| Reference:
|
[3] J. Chauvette F. Stenger: The approximate solution of the nonlinear equation $\Delta u = u - u^3$.J. Math. Anal. Appl. 51 (1975), 229-242. MR 0373320, 10.1016/0022-247X(75)90155-9 |
| Reference:
|
[4] G. H. Ryder: Boundary value problems for a class of nonlinear differential equations.Pacific J. Math. 22 (1967), 477-503. Zbl 0152.28303, MR 0219794, 10.2140/pjm.1967.22.477 |
| Reference:
|
[5] G. Sansone: Su un'equazione differenziale non lineare della fisica nucleare.Istituto Nazionale di Alta Matem. Sympozia Mathematica, Vol. VI, (1970). |
| . |
