Geodesic
On some properties of the solution of the differential equation $u''+\frac{2u'}{r}=u-u^3$
Applications of Mathematics, Tome 35 (1990) no. 4, pp. 315-336
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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 $u(r,\bar{\alpha})$, $u(r,\hat{\alpha})$.
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 $u(r,\bar{\alpha})$, $u(r,\hat{\alpha})$.
DOI : 10.21136/AM.1990.104413
Classification : 34A12, 34C10, 34D05, 34E99, 35Q40
Keywords: spherically symmetric solution; trajectory of the solution; со-limit point of the trajectory; asymptotic formula; antitone and contractive operator; zero of the solution; Klein-Gordon equation; global behavior 
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Šeda, Valter; Pekár, Ján. On some properties of the solution of the differential equation $u''+\frac{2u'}{r}=u-u^3$. Applications of Mathematics, Tome 35 (1990) no. 4, pp. 315-336. doi: 10.21136/AM.1990.104413

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