Three solutions for second-order boundary-value problems with variable exponents

Heidarkhani, Shapour, Razi University, Kermanshah, Iran
Moradi, Shahin, University of Mazandaran
Tersian, Stepan A., University of Ruse, Ruse, Bulgaria

Electron. J. Qual. Theory Differ. Equ. 2018, No. 33, 1-19. DOI: https://doi.org/10.14232/ejqtde.2018.1.33

Communicated by  Bonanno, Gabriele

Received on 2017-12-20 Appeared on 2018-05-26

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Abstract: This paper presents several sufficient conditions for the existence of at least three weak solutions of a nonhomogeneous Neumann problem for an ordinary differential equation with $p(x)$-Laplacian operator. The technical approach is variational, based on a theorem of Bonanno and Candito. An example is also given

Keywords: variable exponent Sobolev spaces, $p(x)$-Laplacian, three weak solutions, variational methods

Mathematics Subject Classification: 34B15, 34L30

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