On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers
We prove that the semilinear elliptic equation −Δu=f(u), in Ω, u=0, on ∂Ω has a positive solution when the nonlinearity f belongs to a class which satisfies μtq≤f(t)≤Ctp at infinity and behaves like tq near the origin, where 1<q<(N+2)/(N−2) if N≥3 and 1<q<+∞ if N=1,2. In our approach, we...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2008-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2008/578417 |
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doaj-312c1ce3baeb4d87980067dcaac7576b2020-11-24T23:09:04ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092008-01-01200810.1155/2008/578417578417On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different PowersClaudianor O. Alves0Marco A. S. Souto1Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, CEP 58.109-970, Campina Grande - PB, BrazilDepartamento de Matemática e Estatística, Universidade Federal de Campina Grande, CEP 58.109-970, Campina Grande - PB, BrazilWe prove that the semilinear elliptic equation −Δu=f(u), in Ω, u=0, on ∂Ω has a positive solution when the nonlinearity f belongs to a class which satisfies μtq≤f(t)≤Ctp at infinity and behaves like tq near the origin, where 1<q<(N+2)/(N−2) if N≥3 and 1<q<+∞ if N=1,2. In our approach, we do not need the Ambrosetti-Rabinowitz condition, and the nonlinearity does not satisfy any hypotheses such those required by the blowup method. Furthermore, we do not impose any restriction on the growth of p.http://dx.doi.org/10.1155/2008/578417 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Claudianor O. Alves Marco A. S. Souto |
| spellingShingle |
Claudianor O. Alves Marco A. S. Souto On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers Abstract and Applied Analysis |
| author_facet |
Claudianor O. Alves Marco A. S. Souto |
| author_sort |
Claudianor O. Alves |
| title |
On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers |
| title_short |
On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers |
| title_full |
On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers |
| title_fullStr |
On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers |
| title_full_unstemmed |
On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers |
| title_sort |
on existence of solution for a class of semilinear elliptic equations with nonlinearities that lies between different powers |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2008-01-01 |
| description |
We prove that the semilinear elliptic equation −Δu=f(u), in Ω, u=0, on ∂Ω has a positive solution when the nonlinearity f belongs to a class which satisfies μtq≤f(t)≤Ctp at infinity and behaves like tq near the origin, where 1<q<(N+2)/(N−2) if N≥3 and 1<q<+∞ if N=1,2. In our approach, we do not need the Ambrosetti-Rabinowitz condition, and the nonlinearity does not satisfy any hypotheses such those required by the blowup method. Furthermore, we do not impose any restriction on the growth of p. |
| url |
http://dx.doi.org/10.1155/2008/578417 |
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AT claudianoroalves onexistenceofsolutionforaclassofsemilinearellipticequationswithnonlinearitiesthatliesbetweendifferentpowers AT marcoassouto onexistenceofsolutionforaclassofsemilinearellipticequationswithnonlinearitiesthatliesbetweendifferentpowers |
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