Existence and multiplicity of solutions for a p(x)-Kirchhoff type equation
Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 95-109.

This paper is concerned with the existence and multiplicity to p(x)-Kirchhoff type problem of the following form

-M(( Ω 1 p(x)|u| p(x) dx) div (|u| p(x)-2 u)=f(x,u)inΩ,
u=0 on Ω.
By means of a direct variational approach and the theory of the variable exponent Sobolev spaces, we establish conditions ensuring the existence and multiplicity of solutions for the problem.

DOI : 10.4171/RSMUP/136-8
Classification : 35
Mots clés : Kirchhoff type problems, $p(x)$-Kirchhoff type, boundary value problem, mountain pass theorem, dual fountain theorem
Afrouzi, Ghasem 1 ; Mirzapour, Maryam 1 ; Chung, Nguyen Thanh 2

1 University of Mazandaran, BABOLSAR, IRAN
2 Quang Binh University, QUANG BINH, VIETNAM
@article{RSMUP_2016__136__95_0,
     author = {Afrouzi, Ghasem and Mirzapour, Maryam and Chung, Nguyen Thanh},
     title = {Existence and multiplicity of solutions for a $p(x)${-Kirchhoff} type equation},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {95--109},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {136},
     year = {2016},
     doi = {10.4171/RSMUP/136-8},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/136-8/}
}
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%A Chung, Nguyen Thanh
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Afrouzi, Ghasem; Mirzapour, Maryam; Chung, Nguyen Thanh. Existence and multiplicity of solutions for a $p(x)$-Kirchhoff type equation. Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 95-109. doi : 10.4171/RSMUP/136-8. http://www.numdam.org/articles/10.4171/RSMUP/136-8/

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