On the existence, uniqueness, and basis properties of radial eigenfunctions of a semilinear second-order elliptic equation in a ball.

Zhidkov, Peter

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The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem ${(φ (u^{'}))}^{'} = λ f (t, u, u^{'})$ , $u (0) = u (T) = A$ . Here $λ$ is the positive parameter, $A > 0$ , $f$ is singular at the value $0$ of its first phase variable and may be singular at the value $A$ of its first and at the value $0$ of its second phase variable.

Weak solutions of a stochastic model for two-dimensional second grade fluids.

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