Electron. J. Diff. Equ., Vol. 2014 (2014), No. 237, pp. 1-12.

Multiple positive solutions for quasilinear elliptic equations of p(x)-Laplacian type with sign-changing nonlinearity

Ky Ho, Chan-Gyun Kim, Inbo Sim

We establish sufficient conditions for the existence of multiple positive solutions to nonautonomous quasilinear elliptic equations with p(x)-Laplacian and sign-changing nonlinearity. For solving the Dirichlet boundary-value problem we use variational and topological methods. The nonexistence of positive solutions is also studied.

Submitted April 15, 2014. Published November 13, 2014.
Math Subject Classifications: 35J20, 35J60, 35J70, 47J10, 46E35.
Key Words: p(x)-Laplacian; variable exponent; sign-changing nonlinearity; positive solutions; multiplicity.

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Ky Ho
Department of Mathematics
University of Ulsan, Ulsan 680-749, Korea
email: hnky81@gmail.com
Chan-Gyun Kim
Department of Mathematics Education
Pusan National University
Busan 609-735, Korea
email: cgkim75@gmail.com
Inbo Sim
Department of Mathematics
University of Ulsan
Ulsan 680-749, Korea
email: ibsim@ulsan.ac.kr

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