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A discontinuous problem with quasilinear operator. (Spanish. English summary) Zbl 1031.35046

Summary: We find conditions on the functions \(q\), \(f\) and \(h\) that allow us to prove the existence of weak solutions to the problem \(-\Delta_pu= h(x) f(u)+ q(x)\) on \(\Omega\); \(u= 0\) on \(\partial\Omega\).

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35J20 Variational methods for second-order elliptic equations
35J60 Nonlinear elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
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