On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity
D. K. Potapov
St. Petersburg State University, Faculty of Applied Mathematics and Control Processes
We consider the question of existence of Dirichlet’s problem solution for the Laplace equation with a spectral parameter and discontinuous
on a phase variable nonlinearity. Using the variational method, we prove a theorem about a number of solutions. We result an example of discontinuous
nonlinearity that satisfies to conditions of the theorem for which there is unique semiregular solution of this boundary problem.
Dirichlet’s problem, the Laplace equation, spectral parameter, discontinuous nonlinearity, variational method, number of solutions.
PDF file (177 kB)
MSC: Primary 35J25; Secondary 35J60
D. K. Potapov, “On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity”, Dal'nevost. Mat. Zh., 12:1 (2012), 86–88
Citation in format AMSBIB
\paper On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity
\jour Dal'nevost. Mat. Zh.
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