Asymptotic behaviour of sign changing radial solutions of Lane Emden Problems in the annulus

Pacella, Filomena; Salazar, Dora

doi:10.3934/dcdss.2014.7.793

Cited by 5 publications

(1 citation statement)

References 7 publications

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“…For Lane-Emden problem (1.2) with Ω be an annulus of R N (N ≥ 2), Grossi [7] derived the asymptotic behavior of the Kazdan-Warner solution and Pacella, Salazar [10] studied asymptotic behaviour of sign changing radial solutions.…”

Section: Weiwei Ao and Chao Liumentioning

confidence: 99%

Asymptotic behavior of sign-changing radial solutions of a semilinear elliptic equation in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^2 $\end{document}</tex-math></inline-formula> when exponent approaches <inline-formula><tex-math id="M2">\begin{document}$ +\infty $\end{document}</tex-math></inline-formula>

Ao¹,

Liu²

2020

Discrete &Amp; Continuous Dynamical Systems - A

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In this paper, we consider a semi-linear elliptic equation in R 2 with the nonlinear exponent approaching infinity. We study asymptotic behavior of sign-changing once radial solutions obtained by . Assuming up(0) > 0, we prove that a suitable rescaling of the positive part u + p converges to the unique regular solution of Liouville equation in R 2 , while a suitable rescaling of the negative part u − p converges to a solution of a singular Liouville equation in R 2 . We also obtain the asymptotic value of the L ∞ -norms of u − p and u + p . Moreover, we show that pup blow up at the origin and pup convergence to the fundamental solution of −∆ + 1 in R 2 (up to a multiplier).

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Section: Weiwei Ao and Chao Liumentioning

confidence: 99%

Asymptotic behavior of sign-changing radial solutions of a semilinear elliptic equation in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^2 $\end{document}</tex-math></inline-formula> when exponent approaches <inline-formula><tex-math id="M2">\begin{document}$ +\infty $\end{document}</tex-math></inline-formula>

Ao¹,

Liu²

2020

Discrete &Amp; Continuous Dynamical Systems - A

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Existence of radial solutions for nonlinear elliptic equations with gradient terms in annular domains

Wei

2019

Nonlinear Analysis

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Morse index of radial nodal solutions of Hénon type equations in dimension two

Santos

Pacella

2017

Commun. Contemp. Math.

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Abstract. We consider non-autonomous semilinear elliptic equations of the typewhere Ω ⊂ R 2 is either a ball or an annulus centered at the origin, α > 0 and f : R → R is C 1,β on bounded sets of R. We address the question of estimating the Morse index m(u) of a sign changing radial solution u. We prove that m(u) ≥ 3 for every α > 0 and that m(u) ≥ α + 3 if α is even. If f is superlinear the previous estimates become m(u) ≥ n(u) + 2 and m(u) ≥ α+n(u)+2, respectively, where n(u) denotes the number of nodal sets of u, i.e. of connected components of {x ∈ Ω; u(x) = 0}. Consequently, every least energy nodal solution uα is not radially symmetric and m(uα) → +∞ as α → +∞ along the sequence of even exponents α.

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Asymptotic behaviour of sign changing radial solutions of Lane Emden Problems in the annulus

Cited by 5 publications

References 7 publications

Existence of radial solutions for nonlinear elliptic equations with gradient terms in annular domains

Morse index of radial nodal solutions of Hénon type equations in dimension two

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