The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term
We show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term ?u+|?u|=p(|x|)f(u,v)?u+|?u|=p(|x|)f(u,v), ?v+|?v|=q(|x|)g(u,v)?v+|?v|=q(|x|)g(u,v) on RNRN, N?3N?3, provided that nonlinearities f and g are positive and continuous, the potentials p...
| Main Authors: | , |
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| Format: | Journal Article |
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Academic Press
2010
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| Online Access: | http://hdl.handle.net/20.500.11937/44021 |
| _version_ | 1848756878468710400 |
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| author | Zhang, Xinguang Liu, L. |
| author_facet | Zhang, Xinguang Liu, L. |
| author_sort | Zhang, Xinguang |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term ?u+|?u|=p(|x|)f(u,v)?u+|?u|=p(|x|)f(u,v), ?v+|?v|=q(|x|)g(u,v)?v+|?v|=q(|x|)g(u,v) on RNRN, N?3N?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. |
| first_indexed | 2025-11-14T09:19:12Z |
| format | Journal Article |
| id | curtin-20.500.11937-44021 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:19:12Z |
| publishDate | 2010 |
| publisher | Academic Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-440212017-09-13T16:05:30Z The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term Zhang, Xinguang Liu, L. Bounded solution Large solution Entire solution Semilinear elliptic problem We show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term ?u+|?u|=p(|x|)f(u,v)?u+|?u|=p(|x|)f(u,v), ?v+|?v|=q(|x|)g(u,v)?v+|?v|=q(|x|)g(u,v) on RNRN, N?3N?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. 2010 Journal Article http://hdl.handle.net/20.500.11937/44021 10.1016/j.jmaa.2010.05.029 Academic Press unknown |
| spellingShingle | Bounded solution Large solution Entire solution Semilinear elliptic problem Zhang, Xinguang Liu, L. The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term |
| title | The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term |
| title_full | The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term |
| title_fullStr | The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term |
| title_full_unstemmed | The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term |
| title_short | The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term |
| title_sort | existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term |
| topic | Bounded solution Large solution Entire solution Semilinear elliptic problem |
| url | http://hdl.handle.net/20.500.11937/44021 |