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On semilinear elliptic equations with indefinite nonlinearities |
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| Authors: | Stanley Alama Gabriella Tarantello |
| Affiliation: | (1) Department of Mathematics, Carnegie Mellon University, 15213 Pittsburgh, PA, USA;(2) Present address: Department of Mathematics and Statistics, McMaster University, L8S-4K1 Hamilton, Ontario, Canada;(3) Present address: Dipartimento di Mathematica, II Università degli Studi di Roma !["ldquo"]("/content/v0v352714080k213/xlarge8220.gif") Tor Vergata!["rdquo"]("/content/v0v352714080k213/xlarge8221.gif") , Via della Ricerca Scientifica, I-00133 Roma, Italy |
| Abstract: | This paper concerns semilinear elliptic equations whose nonlinear term has the formW(x)f(u) whereW changes sign. We study the existence of positive solutions and their multiplicity. The important role played by the negative part ofW is contained in a condition which is shown to be necessary for homogeneousf. More general existence questions are also discussed.Supported in part by NSF grant DMS9003149. |
| Keywords: | 35B32 35J65 35J20 35J25 58E05 |
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