Three positive solutions of nonhomogeneous semilinear elliptic equations (Q878472)

The authors deal with the multiplicity of positive solutions for semilinear elliptic equation \[ -\Delta_x u+ u=|u|^{p- 2}u+ h(z)\quad\text{in }\Omega, \qquad u\in H^1_0(\Omega), \] where \(2< p< {2N\over N-2}\) \((N\geq 3)\), \(\Omega= A\setminus\overline{\mathbb{D}}\) -- infinite cylinder with hole domain and \(h\in L^2(\Omega)\setminus\{0\}\).