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2013•Proceedings of the Royal Society of Edinburgh Section A MathematicsOpen access

On finite Morse index solutions of two equations with negative exponent

Juan Dávila, Dong Ye

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Abstract

We consider the following equations involving negative exponent: where p > 0. Under optimal conditions on the parameters α > −2 and p > 0, we prove the non-existence of finite Morse index solution on exterior domains or near the origin. We also prove an optimal regularity result for solutions with finite Morse index and isolated rupture at 0.

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What this paper is about

We consider the following equations involving negative exponent: where p > 0. Under optimal conditions on the parameters α > −2 and p > 0, we prove the non-existence of finite Morse index solution on exterior domains or near the origin. We also prove an optimal regularity result for solutions with finite Morse index and isolated rupture at 0.

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Available abstract

We consider the following equations involving negative exponent: where p > 0. Under optimal conditions on the parameters α > −2 and p > 0, we prove the non-existence of finite Morse index solution on exterior domains or near the origin. We also prove an optimal regularity result for solutions with finite Morse index and isolated rupture at 0.

Key concepts: Morse code, Exponent, Index (typography), Mathematics, Mathematical analysis, Pure mathematics, Mathematical physics, Applied mathematics

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