On a class of elliptic problems in R2: symmetry and uniqueness results

By J. Prajapat, Gabriella Tarantello. Proceedings of the Royal Society of Edinburgh. Section A Mathematics, 2001

205 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1c7144795a5b18782d0c6fc09cef10a96c602727

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Citations in the corpus

Classification and nondegeneracy of SU(n+1) Toda system with singular sources (2011, background): “it was proved in [34] that any solution u satisfies the following quantization: ∫”
Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS (2010, background): “For N D 2, a similar classification is available for the exponential nonlinearity eU in [44] for ̨ D 0 and in [144] for ̨ > 0.”
Mean field equations, hyperelliptic curves and modular forms: I (2015, background): “A proof can be found in [17, 43, 54], based on the following inequality: For a punctured disk ∆ǫ with a small radius ǫ we have”
Liouville Type Equations with Singular Data¶and Their Applications to Periodic Multivortices¶for the Electroweak Theory (2002, methodology): “λ = V (p), as a limiting equation after blowing up vn around p. All solutions of (10) have been completely classified by Prajapat–Tarantello in [ 43 ].”
Profile of Blow-up Solutions to Mean Field Equations with Singular Data (2004, background): “Notice that, the solution v of (3.3) satisfies (i) R R2 jxj2aev ¼ 8pð1þ aÞ; (ii) vðxÞ ¼ log 1 1þ 1 8ðaþ1Þ2jxj 2ðaþ1Þ 2 ; (cf. Prajapat and Tarantello, 2001), and (1.11) reduces to show, jvkðxÞ vðxÞj C; 8x 2 B 1 ek : To prove Step 1, we fix a small positive number e0 > 0, such that, e0 < 8pða ½a Þ;…”
Some Liouville theorems for Hénon type elliptic equations (2012, background): “When N = 2 and α > −2, it is not difficult to see that any finite Morse index solution is indeed an energy solution, that is |x|αeu ∈ L1(R2); Prajapat & Tarantello [16] have already classified all such solutions.”
Classification of blowup limits for SU(3) singular Toda systems (2013, background): “By the classification result of [Prajapat and Tarantello 2001] we have 2 ∫ R2 h1|y|2γ1ev1 = 8πµ1 and v1(y)=−4µ1 log |y| + O(1), |y|> 1.”