On a problem of lower limit in the study of nonresonance. (English) Zbl 0933.35067

Summary: We prove the solvability of the Dirichlet problem \[ \begin{cases} -\Delta_pu=f(u) +h\quad &\text{in }\Omega,\\ u=0\quad &\text{on }\partial \Omega \end{cases} \] for every given \(h\), under a condition involving only the asymptotic behaviour of the potential \(F\) of \(f\) with respect to the first eigenvalue of the \(p\)-Laplacian \(\Delta_p\). More general operators are also considered.


35J65 Nonlinear boundary value problems for linear elliptic equations
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35A25 Other special methods applied to PDEs
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