POSITIVE SOLUTIONS FOR A CLASS OF p(x)-LAPLACIAN PROBLEMS
2009 ◽
Vol 51
(3)
◽
pp. 571-578
◽
Keyword(s):
AbstractWe consider the system where p(x), q(x) ∈ C1(RN) are radial symmetric functions such that sup|∇ p(x)| < ∞, sup|∇ q(x)| < ∞ and 1 < inf p(x) ≤ sup p(x) < ∞, 1 < inf q(x) ≤ sup q(x) < ∞, where −Δp(x)u = −div(|∇u|p(x)−2∇u), −Δq(x)v = −div(|∇v|q(x)−2∇v), respectively are called p(x)-Laplacian and q(x)-Laplacian, λ1, λ2, μ1 and μ2 are positive parameters and Ω = B(0, R) ⊂ RN is a bounded radial symmetric domain, where R is sufficiently large. We prove the existence of a positive solution when for every M > 0, $\lim_{u \rightarrow +\infty} \frac{h(u)}{u^{p^--1}} = 0$ and $\lim_{u \rightarrow +\infty} \frac{\gamma(u)}{u^{q^--1}} = 0$. In particular, we do not assume any sign conditions on f(0), g(0), h(0) or γ(0).
2004 ◽
Vol 134
(1)
◽
pp. 137-141
◽
2015 ◽
Vol 8
(1)
◽
pp. 19-36
1999 ◽
Vol 42
(2)
◽
pp. 349-374
◽
2006 ◽
Vol 136
(2)
◽
pp. 301-320
1977 ◽
Vol 24
(2)
◽
pp. 234-244
◽
1993 ◽
Vol 35
(1)
◽
pp. 105-113
◽
2010 ◽
Vol 52
(3)
◽
pp. 505-516
◽
Keyword(s):
1998 ◽
Vol 39
(3)
◽
pp. 386-407
◽
2018 ◽
Vol 149
(04)
◽
pp. 939-968