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Some Liouville theorems for Hénon type equations in half-space with nonlinear boundary value conditions and finite Morse indices

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In this paper, we are concerned with Liouville-type theorems for Hénon type equations in half-space with nonlinear boundary value conditions. We prove Liouville-type theorems for solutions belonging to one of the following classes: stable solutions and finite Morse index solutions (whether positive or sign-changing). Our proof is based on a combination of the integral estimates, the Pohozaev-type identity and the monotonicity formula of solutions and blowing down sequence.

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  1. Faculté des Sciences, Département de Mathématiques, Université de Sfax, B.P 1171, Sfax, 3000, Tunisia

    Belgacem Rahal

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  1. Belgacem Rahal
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Rahal, B. Some Liouville theorems for Hénon type equations in half-space with nonlinear boundary value conditions and finite Morse indices. Anal.Math.Phys. 10, 53 (2020). https://doi.org/10.1007/s13324-020-00398-9

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  • DOI: https://doi.org/10.1007/s13324-020-00398-9

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