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singular Dirichlet boundary value problem; dead core; positive solution; dead core solution; pseudodead core solution; existence; $\phi $-Laplacian
The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem $(\phi (u'))' = \lambda f(t,u,u')$, $u(0)=u(T)=A$. Here $\lambda $ 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.
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