1993
DOI: 10.1017/s1446788700037150
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Generalized Emden-Fowler equations of subcritical growth

Abstract: The existence of positive solutions, vanishing at infinity, for the semilinear eigenvalue problem Lu = X • f(x, y) in R^ is obtained, where L is a strictly elliptic operator. The function / is assumed to be of subcritical growth with respect to the variable u .

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Cited by 3 publications
(5 citation statements)
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“…The assertion follows directly from the regularity result of TOLKSDORF 181. wheref; and y i fulfil the same conditions as g and y, respectively, with some 0 < 6, < 00, i = 1, ..., I. The assertion like Theorem 3.1 concerning this problem should be the generalization of previous results of NOUSSAIR and SWANSON [5] and ROTHEK [6] concerning the Emden-Fowler equation. where !…”
Section: -R ' Xmentioning
confidence: 51%
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“…The assertion follows directly from the regularity result of TOLKSDORF 181. wheref; and y i fulfil the same conditions as g and y, respectively, with some 0 < 6, < 00, i = 1, ..., I. The assertion like Theorem 3.1 concerning this problem should be the generalization of previous results of NOUSSAIR and SWANSON [5] and ROTHEK [6] concerning the Emden-Fowler equation. where !…”
Section: -R ' Xmentioning
confidence: 51%
“…D R~B E K [2], LAO SEN YU [4] for the references). F o r p = 2, we obtain in (1.1) the generalized Emden-Fowler equation which was studied recently by NOUSSAIR and SWANSON [5] and ROTHER [6]. Note that the equation of the type (1.1) is very close to applications.…”
Section: Introductionmentioning
confidence: 54%
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“…In [7], the equation ( 1) has been considered in the case of constant exponent. While in [3], Fan, Zhang and Zhao showed that the problem…”
Section: Introductionmentioning
confidence: 99%
“…In this method, one must assume in general that the nonlinearity f satisfies the (AR) condition. The author in [7] discovered a new functional whose critical point is a solution of problem (1) in the special case p(x) = p =constant.…”
Section: Introductionmentioning
confidence: 99%