The author considers the equation of the semiclassical, nonlinear Schrödinger type: \[ -\Delta u(x)+q(x)| u(x)| ^{p-2}u(x)+f_0(x,u(x))=h(x),\;\;x\in\Omega\subset\mathbb R^n,\;n\geq 1, \] subject to \(u(x)\big| _{x\in\partial\Omega}=0\), with the assumptions \(q\in W_{p_0}^{-1}(\Omega)\), \(p_0>p>2\), \(f_0\) is the Caratheodory function and \(h\in W_{p_0}^{-1}(\Omega)\). The main theorem states that the described problem, with some additional assumptions, is solvable in \(\overset {0} W_2^1(\Omega)\).