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Existence and multiplicity of the solutions of the p(x)–Kirchhoff type equation via genus theory

✍ Scribed by Mustafa Avci; Bilal Cekic; Rabil A. Mashiyev

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
175 KB
Volume
34
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Paper 1. Introduction

We are concerned with the following p.x/-Kirchhoff type equation

where R N is a bounded smooth domain, p 2 C with 1 < p .x/ < N. We assume that M and f satisfy the following conditions:

.M 1 / M : R C ! R C is a continuous function and satisfies the (polynomial growth) condition

for all t > 0 and m 1 , m 2 real numbers such that 0 < m 1 Ä m 2 and ˛ ˇ> 1;

.

x/ 1 , for all t 0 and for all x 2 , where C 1 , C 2 are positive constants and s, q 2 C such that 1 < s.x/ < q.x/ < p .x/ D .Np.x//=.N p.x// for all x 2 ;

.f 2 / f is an odd function according to t, that is, f .x, t/ D f .x, t/

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