Density of the range of a wave operator with nonmonotone superlinear nonlinearity
Consider the nonlinear wave equation \(u_{tt}-u_{xx}+g(w)=f(x,t)\), \((x,t)t(0,\pi)\times R\), \(u(0,t)=u(\pi,t)=0\), \(t\in R\); \(u(x,t+T)=u(x,t)\), \((x,t)\in (0,\pi)\times R\). Many authors were concerned with this problem, for example, the author [(*) Tokyo J. Math. 8, 377-387 (1985; Zbl 0607.35063)]. This paper is an extension of (*) to the case that g(s) is superlinear.
scientific article; zbMATH DE number 4065539
scientific article