Asymptotic behavior of positive solution branches of elliptic problems with linear part at resonance (Q1198203)

In this interesting paper, the authors investigate the existence of solutions of \(\Delta u+\lambda_ 1 u+g(u)=h(x)\) in \(\Omega\), where \(\lambda_ 1\) denotes the first eigenvalue of the Laplacian for Dirichlet boundary conditions, \(\varphi_ 1\) is the corresponding eigenfunction , \(\int_ \Omega h\varphi_ 1=0\), \(g\) is bounded and oscillatory and \(\Omega\) is usually assumed convex. This involves a careful asymptotic analysis of certain integrals. The results improve some of the results of the reviewer [Ann. Mat. Pura Appl., IV. Ser. 131, 167-185 (1982; Zbl 0519.34011)].