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 .

Nonlinear Eigenvalue Problem for p‐Laplacian in IRN

“…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 !…”

“…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.…”

“…Step 1. (This step follows the lines of the proof of Theorem 1 in ROTHER [6] for the case p = 2. For the completeness and for the reader's convenience we present it here in detail.)…”

Nonlinear Eigenvalue Problem Without Ambrosetti and Rabinowitz Condition: An Orlicz Space Setting

“…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…”

“…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.…”