Electron. J. Diff. Eqns., Vol. 2008(2008), No. 98, pp. 1-10.

### Existence of solutions for a resonant problem under Landesman-Lazer conditions Quoc Anh Ngo, Hoang Quoc Toan

Abstract:
This article shows the existence of weak solutions in to a class of Dirichlet problems of the form

in a bounded domain of . Here a satisfies

for all , a.e. , , , for a.e. x in ; is the first eigenvalue for on with zero Dirichlet boundary condition and g, h satisfy some suitable conditions.

Submitted March 24, 2008. Published July 25, 2008.
Math Subject Classifications: 35J20, 35J60, 58E05.
Key Words: p-Laplacian; Non-uniform; Landesman-Laser type; Divergence form.

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 Quocc Anh Ngo Department of Mathematics, College of Science Vietnam National University, Hanoi, Vietnam email: bookworm_vn@yahoo.com, nqanh@vnu.edu.vn Hoang Quoc Toan Department of Mathematics, College of Science Vietnam National University, Hanoi, Vietnam email: hq_toan@yahoo.com
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