Abstract
Semiregular solutions of integral equations with discontinuous nonlinearities were introduced byKrasnosel'skii and Pokrovskii in [i], where they also obtained sufficient conditions for the existence of such solutions. In the present paper we obtain a theorem on the existence of semiregular solutions of the Dirichlet problem for quasilinear equations of elliptic type with discontinuous weak nonlinearities. The proof is based on a general result of the author in [2] concerning equations with discontinuous operators in Banach spaces. In contrast to [I], it is not assumed that a nonlinearity of f(x, y) appearing in the equation is monotone in u; in addition, the restrictions on the growth of f(x, u) are weakened. i. Formulation of the Principal Result. We consider the Dirichlet problem
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