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The existence of a nontrivial solution to the -Laplacian problem with nonlinearity asymptotic to at infinity in

✍ Scribed by Chengjun He; Gongbao Li

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
358 KB
Volume
68
Category
Article
ISSN
0362-546X

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We prove the existence of a non-trivial weak solution for the equation by variational methods. We consider the case where a = Ξ» 1 or b = Ξ» 1 (Ξ» 1 denotes the first eigenvalue of -βˆ† p ), or the case where a is close to b, while the nonlinearity f belongs to a class that contains, for example, |u| q-

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We prove the existence of a non-trivial weak solution for the equation by variational methods. We consider the case where a = Ξ» 1 or b = Ξ» 1 , while the nonlinearity f belongs to a class that contains, for example, |u| q-2 u (1 < q < p).