A Necessary and Sufficient Condition of Nonresonance for a Semilinear Neumann Problem
A Necessary and Sufficient Condition of Nonresonance for a Semilinear Neumann Problem
We consider the Neumann problem \[ \left \{ {\begin {array}{*{20}{c}} { - \Delta u = g(u) + h(x){\text { in }}\Omega ,} \\ {\partial u/\partial \nu = 0\quad {\text {on }}\operatorname {bdry} \Omega .} \\ \end {array} } \right .\] Assuming some growth restriction on the nonlinearity $g$, we prove …