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  • 1 Department of Mathematics and Informatics, Quang Binh University, 312 Ly Thuong Kiet, Dong Hoi, Vietnam
  • 2 Faculty of Mathematics, Mechanics and Informatics, University of Natural Sciences, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam
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Abstract.

We consider the p-Laplacian type elliptic problem

ea
where Ω=Ω1×Ω2⊂ℝN is a bounded domain having cylindrical symmetry, Ω1⊂ℝm is a bounded regular domain and Ω2 is a k-dimensional ball of radius R, centered in the origin and m+k=N, m≧1, k≧2. Under some suitable conditions on the functions a and h, using variational methods we prove that the problem has at least one resp. at least two solutions in two cases: g=0 and g≠0.

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