Singular solutions of elliptic equations involving nonlinear gradient terms on perturbations of the ball |
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Authors: | A. Aghajani C. Cowan S.H. Lui |
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Affiliation: | 1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran;2. Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada |
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Abstract: | In this article we obtain positive singular solutions of (1) where Ω is a small perturbation of the unit ball in . For we prove that if Ω is a sufficiently small perturbation of the unit ball there exists a singular positive weak solution u of (1). In the case of we prove a similar result but now the positive weak solution u is contained in and yet is not in for any . |
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Keywords: | Corresponding author. |
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