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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.

MSC:

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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