Abstract
This work is devoted to obtain the \(L^p\) and the \(L^{\infty }\)-estimates of solutions via their Morse indices to the following m-Laplacian problems
where \(\Omega \subset {\mathbf {R}}^N\) is a bounded domain with smooth boundary, \(N>m>2\) and \(f\in C(\overline{\Omega }\times {\mathbb {R}})\) which will be specified later. As far as we know, it seems to be the first time that such explicit estimates are obtained for a nonlinear degenerate problems. So, our main results extend and complement previously \(L^{\infty }\)-estimates results in the literature.
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Acknowledgements
The authors would like to express their appreciation to the anonymous referees for useful comments and valuable suggestions which help us in depth to improve the presentation of paper. The first author would like to express his deepest gratitude to the Military School of Aeronautical Specialties, Sfax (ESA) for providing us with an excellent atmosphere for doing this work. This work was partially done while the second author was visited the I.C.T.P, in July 2017.
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Hamdani, M.K., Harrabi, A. \(L^\infty \)-Norm Estimates of Weak Solutions via Their Morse Indices for the m-Laplacian Problems. Results Math 74, 69 (2019). https://doi.org/10.1007/s00025-019-0986-y
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DOI: https://doi.org/10.1007/s00025-019-0986-y