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2, 447–460. [3] J. E. Brothers, W. P. Ziemer, Minimal rearrangements of Sobolev functions, 15th winter school in abstract analysis (Srn´ı, 1987), Acta Univ. Carolin. Math. Phys, 28 (1987), no. 2, 13–24. [4] F. -Q. Wang, Nonlinear elliptic equations on expanding symmetric domains, J. Differential Equations, 156 (1999), no. 1, 153–181. [5] F. -Q. Wang, On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions, Comm. Pure Appl.

Peral, Hardy Inequalities and some critical elliptic and parabolic problems, J. Diff. Equations, 144 (1998), no. 2, 441–476. [19] C. E. Guti´ errez, Harnack’s inequality for degenerate Schr¨ odinger operators, Trans. Amer. Math. , 312 (1989), no. 1, 403–419. [20] E. Jannelli, The role played by space dimension in elliptic critical problems, J. Differential Equations, 156 (1999), no. 2, 407–426. [21] L. D. Landau, E. M. , London-Paris, 1965. [22] P. L. Lions, The concentration-compactness principle in the calculus of variations.

27] M. Struwe, Variational Methods and Applications to Nonlinear Partial Differential Equations and Hamiltonian systems, Springer-Verlag, Berlin/New York (1990). [28] S. Terracini, On positive entire solutions to a class of equations with singular coefficient and critical exponent, Adv. Diff. , 1 (1996), no. 2, 241–264. -Q. Wang, Existence and symmetry of multi-bump solutions for nonlinear Schrdinger equations, J. Differential Equations, 159 (1999), no. 1, 102–137. [30] M. Willem, Minimax theorems, Progress in Nonlinear Differential Equations and their Applications, 24.

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INSTRUCTOR'S SOLUTIONS MANUAL (to accompany Elementary Statistics Ninth Edition) by MILTON LOYER


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