On a class of semilinear elliptic equations with boundary conditions and potentials which change sign
We study the existence of nontrivial solutions for the problem Δu=u, in a bounded smooth domain Ω⊂ℝℕ, with a semilinear boundary condition given by ∂u/∂ν=λu−W(x)g(u), on the boundary of the domain, where W is a potential changing sign, g has a superlinear growth condition, and the parameter λ∈]0,λ1]...
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Hindawi Limited
2005-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA.2005.95 |
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doaj-166a253bdf44480791d664d3b756e5e82020-11-24T21:54:34ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092005-01-01200529510410.1155/AAA.2005.95On a class of semilinear elliptic equations with boundary conditions and potentials which change signM. Ouanan0A. Touzani1Department of Mathematics and Informatics, Faculty of Sciences Dhar-Mahraz, P.O. Box 1796 Atlas-Fez, Fez, MoroccoDepartment of Mathematics and Informatics, Faculty of Sciences Dhar-Mahraz, P.O. Box 1796 Atlas-Fez, Fez, MoroccoWe study the existence of nontrivial solutions for the problem Δu=u, in a bounded smooth domain Ω⊂ℝℕ, with a semilinear boundary condition given by ∂u/∂ν=λu−W(x)g(u), on the boundary of the domain, where W is a potential changing sign, g has a superlinear growth condition, and the parameter λ∈]0,λ1];λ1 is the first eigenvalue of the Steklov problem. The proofs are based on the variational and min-max methods.http://dx.doi.org/10.1155/AAA.2005.95 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. Ouanan A. Touzani |
| spellingShingle |
M. Ouanan A. Touzani On a class of semilinear elliptic equations with boundary conditions and potentials which change sign Abstract and Applied Analysis |
| author_facet |
M. Ouanan A. Touzani |
| author_sort |
M. Ouanan |
| title |
On a class of semilinear elliptic equations with boundary conditions and potentials which change sign |
| title_short |
On a class of semilinear elliptic equations with boundary conditions and potentials which change sign |
| title_full |
On a class of semilinear elliptic equations with boundary conditions and potentials which change sign |
| title_fullStr |
On a class of semilinear elliptic equations with boundary conditions and potentials which change sign |
| title_full_unstemmed |
On a class of semilinear elliptic equations with boundary conditions and potentials which change sign |
| title_sort |
on a class of semilinear elliptic equations with boundary conditions and potentials which change sign |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2005-01-01 |
| description |
We study the existence of nontrivial solutions for the problem Δu=u, in a bounded smooth domain Ω⊂ℝℕ, with a semilinear boundary condition given by ∂u/∂ν=λu−W(x)g(u), on the boundary of the domain, where W is a potential changing sign, g has a superlinear growth condition, and the parameter λ∈]0,λ1];λ1 is the first eigenvalue of the Steklov problem. The proofs are based on the variational and min-max methods. |
| url |
http://dx.doi.org/10.1155/AAA.2005.95 |
| work_keys_str_mv |
AT mouanan onaclassofsemilinearellipticequationswithboundaryconditionsandpotentialswhichchangesign AT atouzani onaclassofsemilinearellipticequationswithboundaryconditionsandpotentialswhichchangesign |
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1725867166983520256 |