Multiple positive and sign-changing solutions for a singular Schrödinger equation with critical growth

Bahri, 1988, On a nonlinear elliptic equation involving the Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math., 41, 253, 10.1002/cpa.3160410302 Benci, 1990, Existence of positive solutions of the equation in -Δu+a(x)u=u(N+2)/(N-2) in RN, J. Funct. Anal., 88, 90, 10.1016/0022-1236(90)90120-A Brezis, 1983, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc., 88, 486, 10.2307/2044999 Brezis, 1983, Positive solutions of nonlinear elliptic equations involving critical exponents, Comm. Pure Appl. Math., 34, 437, 10.1002/cpa.3160360405 Cao, 1995, Multiple positive and nodal solutions for semilinear elliptic problems with critical exponets, Indiana Univ. Math. J., 44, 1249, 10.1512/iumj.1995.44.2027 Chabrowski, 1999 Chabrowski, 2002, On a semilinear Schrödinger equation with critical Sobolev exponent, Proc. Amer. Math. Soc., 130, 85, 10.1090/S0002-9939-01-06143-3 Chen, 2004, Exact local behavior of positive solutions for a semilinear elliptic equation with Hardy term, Proc. Amer. Math. Soc., 132, 3225, 10.1090/S0002-9939-04-07567-7 Chen, 2005, Multiple positive solutions for a semilinear equation with prescribed singularity, J. Math. Anal. Appl., 305, 140, 10.1016/j.jmaa.2004.10.057 J. Chen, S. Li, Y. Li, Multiple solutions for a semilinear equation involving singular potential and critical exponent, Z. Angew. Math. Phys., in press. Chou, 1993, On the best constant for a weighted Sobolev–Hardy inequality, J. London Math. Soc., 48, 137, 10.1112/jlms/s2-48.1.137 Ferrero, 2001, Existence of solutions for singular critical growth semilinear elliptic equations, J. Differential Equations, 177, 494, 10.1006/jdeq.2000.3999 Jannelli, 1999, The role played by space dimension in elliptic critical problems, J. Differential Equations, 156, 407, 10.1006/jdeq.1998.3589 Passaseo, 1989, Multiplicity of positive solutions of nonlinear elliptic equations with critical exponents in some contractible domains, Manuscripta Math., 65, 147, 10.1007/BF01168296 Rabinowitz, 1992, On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys., 43, 270, 10.1007/BF00946631 Strauss, 1977, Existence of solitary waves in higher dimensions, Comm. Math. Phys., 55, 149, 10.1007/BF01626517 Tarantello, 1992, On nonhomogeneous elliptic involving critical sobolev exponent, Ann. Inst. H. Poincaré Anal. Non Lineairé, 9, 281, 10.1016/S0294-1449(16)30238-4 Tarantello, 1993, Multiplicity results for an inhomogeneous Neumann problem with critical exponent, Manuscripto Math., 81, 51 Terracini, 1996, On positive entire solutions to a class of equations with singular coefficient and critical exponent, Adv. Differential Equation, 1, 241, 10.57262/ade/1366896239 Wang, 1999, Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations, J. Differential Equations, 159, 102, 10.1006/jdeq.1999.3650 Wang, 2001, Singular minimization problems, J. Differential Equations, 161, 307, 10.1006/jdeq.1999.3699 Willem, 1996