Unbounded viscosity solutions of nonlinear second order PDE's (Q2733857)

The authors deal with the following nonlinear second-order partial differential equations NEWLINE\[NEWLINE\lambda u+ F(x,Du,\Delta^2 u)- f(x)= 0\quad\text{in }\mathbb{R}^N\tag{1}NEWLINE\]NEWLINE and NEWLINE\[NEWLINE\begin{cases} u_t+ G(t,x,Du, D^2u)- g(t,x)= 0\quad\text{in }(0,T)\times \mathbb{R}^N,\\ u(0,x)= \psi(x),\end{cases}\tag{2}NEWLINE\]NEWLINE where \(\lambda, T>0\) are constants, \(F\) and \(G\) are degenerate elliptic operators, \(f\), \(g\), and \(\psi\) are given functions. They prove the uniqueness and existence of unbounded viscosity solutions of (1) and (2), where nonlinear terms behave like polynomials. Moreover, optimality of the growth conditions is discussed.