The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term |
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Authors: | Xinguang Zhang Lishan Liu |
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Affiliation: | a School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, Shandong, People's Republic of China b School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, People's Republic of China |
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Abstract: | We show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term Δu+|∇u|=p(|x|)f(u,v), Δv+|∇v|=q(|x|)g(u,v) on RN, N?3, provided that nonlinearities f and g are positive and continuous, the potentials p and q are continuous, c-positive and satisfy appropriate growth conditions at infinity. We find that entire large positive solutions fail to exist if f and g are sublinear and p and q have fast decay at infinity, while if f and g satisfy some growth conditions at infinity, and p, q are of slow decay or fast decay at infinity, then the system has infinitely many entire solutions, which are large or bounded. |
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Keywords: | Large solution Semilinear elliptic problem Bounded solution Entire solution |
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