Chapter 1 Research background Chapter 2 Sign-changing solutions for quasilinear Schr?dinger-Poisson system 2.1 Main results 2.2 Preliminary results 2.3 Proof of main results Chapter 3 Multiple solutions for quasilinear Schr?dinger-Poisson system 3.1 Main results 3.2 Preliminary results 3.3 Proof of main results Chapter 4 Sign-changing solutions for quasilinear Kirchhoff-Schr?dinger-Poisson system 4.1 Main results 4.2 Preliminary results 4.3 Proof of main results Chapter 5 Schr?dinger problems involving the Sobolev-Hardy exponent 5.1 Main results 5.2 The first solution 5.3 The second solution References