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EXISTENCE RESULT FOR NONUNIFORMLY DEGENERATE SEMILINEAR ELLIPTIC SYSTEMS IN N

Published online by Cambridge University Press:  01 September 2009

NGUYEN THANH CHUNG  and
HOANG QUOC TOAN
NGUYEN THANH CHUNG
Affiliation:
Department of Mathematics and Informatics, Quang Binh University, 312 Ly Thuong Kiet, Dong Hoi, Vietnam e-mail: ntchung82@yahoo.com
HOANG QUOC TOAN
Affiliation:
Department of Mathematics, Hanoi University of Science, 334 Nguyen Trai, Hanoi, Vietnam e-mail: hq_toan@yahoo.com
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Abstract

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We study the existence of solutions for a class of nonuniformly degenerate elliptic systems in N, N ≥ 3, of the form where hi ∈ L1loc(N), hi(x) ≧ γ0|x|α with α ∈ (0, 2) and γ0 > 0, i = 1, 2. The proofs rely essentially on a variant of the Mountain pass theorem (D. M. Duc, Nonlinear singular elliptic equations, J. Lond. Math. Soc. 40(2) (1989), 420–440) combined with the Caffarelli–Kohn–Nirenberg inequality (First order interpolation inequalities with weights, Composito Math. 53 (1984), 259–275).

Keywords

35J6535J20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 3 , September 2009 , pp. 561 - 570
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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