Monotonicity methods for two classes of nonlinear boundary value problems with semilinear first order elliptic systems in the plane. (English) Zbl 0534.35015
In a preceding paper [Math. Nachr. 100, 187-212 (1981; Zbl 0473.35065)] the author applied monotonicity methods and Hammerstein integral equation theory for proving existence and uniqueness of solutions to a class of boundary value problems for a semilinear complex first-order differential equation of the form
\[
\partial w/\partial \bar z-a(z)\bar w=F(z)+H(z,w),
\]
in the unit disc or in an annulus, with linear boundary conditions of Riemann-Hilbert type. Those investigations are now extended to the case of nonlinear boundary conditions of Riemann-Hilbert type and to related problems involving generalized Steklov boundary conditions.
Reviewer: M.Kracht
MSC:
| 35F30 | Boundary value problems for nonlinear first-order PDEs |
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 35Q15 | Riemann-Hilbert problems in context of PDEs |
| 30E25 | Boundary value problems in the complex plane |
Keywords:
monotonicity methods; nonlinear boundary value problems; semilinear first order elliptic systems in the plane; complex differential equation; boundary conditions of Riemann-Hilbert or Steklov type; Hammerstein integral equationCitations:
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