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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Conformal metrics on $\mathbb{R}^{2m}$ with constant Q-curvature, prescribed volume and asymptotic behavior
Pages: 283 - 299, Issue 1, January 2015

doi:10.3934/dcds.2015.35.283      Abstract        References        Full text (458.7K)           Related Articles

Ali Hyder - University of Basel, Department of Mathematics and Computer Science, Rheinsprung 21, 4051 Basel, Switzerland (email)
Luca Martinazzi - University of Basel, Department of Mathematics and Computer Science, Rheinsprung 21, 4051 Basel, Switzerland (email)

1 H. Brézis and F. Merle, Uniform estimates and blow-up behavior for solutions of $-\Delta u=V(x)e^u$ in two dimensions, Comm. Partial Differential Equations, 16 (1991), 1223-1253.       
2 Sun-Yung A. Chang and W. Chen, A note on a class of higher order conformally covariant equations, Discrete Contin. Dynam. Systems, 7 (2001), 275-281.       
3 Sun-Yung A. Chang and P. Yang, On uniqueness of solutions of $n$-th order differential equations in conformal geometry, Math. Res. Lett., 4 (1997), 91-102.       
4 W. Chen and C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J., 63 (1991), 615-622.       
5 D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Reprint of the 1998 edition, Classics in Mathematics, Springer-Verlag, Berlin, 2001.       
6 E. A. Gorin, Asymptotic properties of polynomials and algebraic functions of several variables, Russ. Math. Surv., 16 (1961), 91-118.       
7 C. R. Graham, R. Jenne, L. Mason and G. Sparling, Conformally invariant powers of the Laplacian. I. existence, J. London Math. Soc., 46 (1992), 557-565.       
8 T. Jin, A. Maalaoui, L. Martinazzi and J. Xiong, Existence and asymptotics for solutions of a non-local Q-curvature equation in dimension three, to appear in Calc. Var. Partial Differential Equations, (2014).
9 C. S. Lin, A classification of solutions of a conformally invariant fourth order equation in $\mathbbR^n$, Comment. Math. Helv., 73 (1998), 206-231.       
10 R. C. McOwen, The behavior of the Laplacian on weighted Sobolev spaces, Comm. Pure Appl. Math., 32 (1979), 783-795.       
11 L. Martinazzi, Conformal metrics on $\mathbbR^{2m}$ with constant $Q$-curvature, Rend. Lincei. Mat. Appl., 19 (2008), 279-292.       
12 L. Martinazzi, Classification of solutions to the higher order Liouville's equation on $\mathbbR^{2m}$, Math. Z., 263, (2009), 307-329.       
13 L. Martinazzi, Quantization for the prescribed Q-curvature equation on open domains, Commun. Contemp. Math., 13 (2011), 533-551.       
14 L. Martinazzi, Conformal metrics on $\mathbbR^{2m}$ with constant Q-curvature and large volume, Ann. Inst. Henri Poincaré (C), 30 (2013), 969-982.       
15 L. Martinazzi and M. Petrache, Asymptotics and quantization for a mean-field equation of higher order, Comm. Partial Differential Equations, 35 (2010), 443-464.       
16 F. Robert, Quantization effects for a fourth order equation of exponential growth in dimension four, Proc. Roy. Soc. Edinburgh Sec. A, 137 (2007), 531-553.       
17 J. Wei and D. Ye, Nonradial solutions for a conformally invariant fourth order equation in $\mathbbR^4$, Calc. Var. Partial Differential Equations, 32 (2008), 373-386.       

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