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On the Existence of Positive Decaying Entire Solutions for a Class of Sublinear Elliptic Equations

Published online by Cambridge University Press:  20 November 2018

Yasuhiro Furusho  and
Takaŝi Kusano
Yasuhiro Furusho
Affiliation:
Saga University, Saga, Japan
Takaŝi Kusano
Affiliation:
Hiroshima University, Hiroshima, Japan
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In recent years there has been a growing interest in the existence and asymptotic behavior of entire solutions for second order nonlinear elliptic equations. By an entire solution we mean a solution of the elliptic equation under consideration which is guaranteed to exist in the whole Euclidean N-space RN, N ≧ 2. For standard results on the subject the reader is referred to the papers [2-7, 9-21].

The study of entire solutions, which at an early stage was restricted to simple equations of the form Δu + f(x, u) = 0, x ∊ RN, Δ being the N-dimensional Laplacian, has now been extended and generalized to elliptic equations of the type

A

where

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 5 , 01 October 1988 , pp. 1156 - 1173
Copyright
Copyright © Canadian Mathematical Society 1988

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