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Solutions of elliptic problems of p-Laplacian type in a cylindrical symmetric domain

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Abstract.

We consider the p-Laplacian type elliptic problem

$$\begin{cases}- \operatorname{div}\, (a(x,\nabla u)) = h(x) {|u|}^{q-2}u +g(x) & \text{in \ } \Omega,\\u = 0 & \text{in \ } \partial\Omega,\end{cases}$$

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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Authors and Affiliations

  1. Department of Mathematics and Informatics, Quang Binh University, 312 Ly Thuong Kiet, Dong Hoi, Vietnam

    Nguyen Thanh Chung

  2. Faculty of Mathematics, Mechanics and Informatics, University of Natural Sciences, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Hoang Quoc Toan

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  1. Nguyen Thanh Chung
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  2. Hoang Quoc Toan
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Correspondence to Nguyen Thanh Chung.

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Chung, N.T., Toan, H.Q. Solutions of elliptic problems of p-Laplacian type in a cylindrical symmetric domain. Acta Math Hung 135, 42–55 (2012). https://doi.org/10.1007/s10474-011-0163-6

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  • DOI: https://doi.org/10.1007/s10474-011-0163-6

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