## Taiwanese Journal of Mathematics

### EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR DEGENERATE $p(x)$-LAPLACE EQUATIONS INVOLVING CONCAVE-CONVEX TYPE NONLINEARITIES WITH TWO PARAMETERS

#### Abstract

We show the existence of two nontrivial nonnegative solutions and infinitely many solutions for degenerate $p(x)$-Laplace equations involving concave-convex type nonlinearities with two parameters. By investigating the order of concave and convex terms and using a variational method,  we determine the existence according to the range of each parameter. Some Caffarelli-Kohn-Nirenberg type problems with variable exponents are also discussed.

#### Article information

Source
Taiwanese J. Math. Volume 19, Number 5 (2015), 1469-1493.

Dates
First available in Project Euclid: 4 July 2017

https://projecteuclid.org/euclid.twjm/1499133719

Digital Object Identifier
doi:10.11650/tjm.19.2015.5187

#### Citation

Ho, Ky; Sim, Inbo. EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR DEGENERATE $p(x)$-LAPLACE EQUATIONS INVOLVING CONCAVE-CONVEX TYPE NONLINEARITIES WITH TWO PARAMETERS. Taiwanese J. Math. 19 (2015), no. 5, 1469--1493. doi:10.11650/tjm.19.2015.5187. https://projecteuclid.org/euclid.twjm/1499133719

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