Four solutions of an inhomogeneous elliptic equation with critical exponent and singular term. (English) Zbl 1170.35430

Summary: We prove the existence of four nontrivial solutions of \[ -\Delta u - \frac{\lambda }{|x|^2}u = |u|^{2^*-2}u + \mu |x|^{\alpha -2}u + f(x),\qquad x\in \varOmega \setminus \{0\} \] and show that at least one of them is sign changing. Our results extend some previous works, such as [G. Tarantello, Manuscr. Math. 81, No. 1–2, 57–78 (1993; Zbl 0831.35066); D. Kang and Y. Deng, Nonlinear Anal., Theory Methods Appl. 60, No. 4 (A), 729–753 (2005; Zbl 1163.35378); N. Hirano and N. Shioji, Proc. R. Soc. Edinb., Sect. A, Math. 137, No. 2, 333–347 (2007; Zbl 1221.35148)].


35J70 Degenerate elliptic equations
35J20 Variational methods for second-order elliptic equations
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