Taiwanese Journal of Mathematics


Ky Ho and Inbo Sim

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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.

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

First available in Project Euclid: 4 July 2017

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Primary: 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations 35J70: Degenerate elliptic equations 47J10: Nonlinear spectral theory, nonlinear eigenvalue problems [See also 49R05] 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

$p(x)$-Laplacian weighted variable exponent Lebesgue-Sobolev spaces concave-convex nonlinearities nonnegative solutions multiplicity


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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