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Keywords:
quasilinear elliptic; integral operators; fixed points theory
quasilinear elliptic; integral operators; fixed points theory
Summary:
The existence of decaying positive solutions in ${\Bbb R}_+$ of the equations $(E_\lambda )$ and $(E_\lambda^1)$ displayed below is considered. From the existence of such solutions for the subhomogeneous cases (i.e. $t^{1-p} F(r,tU,t|U'|) \searrow 0$ as $t \nearrow \infty $), a super-sub-solutions method (see \S\,2.2) enables us to obtain existence theorems for more general cases.
References:
[1] Hardy G.H et al.: Inegalities. Cambridge Press (1934).
[2] Istratescu V.I.: Fixed Point Theory. Math. and its Appl., Reidel Publ. (1981). MR 0620639 | Zbl 0465.47035
[3] Kawano N., Yanagida E., Yotsutani S.: Structure theorems for positive radial solutions to $ {div} (|Du|^{m-2} Du) + K(|x|)u^q =0$ in ${\Bbb R}^n$. J. Math. Soc. Japan 45 no. 4 (1993), 719-742. MR 1239344 | Zbl 0803.35040
[4] Kusano T., Swanson C.A.: Radial entire solutions of a class of quasilinear elliptic equations. J.D.E. 83 (1990), 379-399. MR 1033194 | Zbl 0703.35060
[5] Tadie: Weak and classical positive solutions of some elliptic equations in ${\Bbb R}^n$, $n\geq 3$: radially symmetric cases. Quart. J. Oxford 45 (1994), 397-406. MR 1295583
[6] Tadie: Subhomogeneous and singular quasilinear Emden-type ODE. to appear. Zbl 1058.34505
[7] Yasuhiro F., Kusano T., Akio O.: Symmetric positive entire solutions of second order quasilinear degenerate elliptic equations. Arch. Rat. Mech. Anal. 127 (1994), 231-254. MR 1288603 | Zbl 0807.35035
[8] Yin Xi Huang: Decaying positive entire solutions of the p-Laplacian. Czech. Math. J. 45 no. 120 (1995), 205-220. MR 1331458
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