Coercive solvability of a generalized nonlinear Cauchy-Riemann system (Q1363949)

Let \(A,R:L_2(\mathbb{C})\to L_{\infty,\text{loc}}(\mathbb{C})\) be nonlinear operators, \((Bw)(z)= b(z,\text{Re }w(z),\text{Im }w(z))\), \(b(z,\zeta,\eta)\in C^1(\mathbb{C}\times\mathbb{R}\times\mathbb{R})\). In this paper, the coercive properties of the equation \[ \partial_{\overline z}w+ wAw+\overline wBw+\overline wRw=f,\quad w,f\in L_2(\mathbb{C}) \] are studied.