Solvability for Certain Superlinear Elliptic Equation Boundary Value Problem with Parameter
In this paper,we study the solvability of a class of Dirichlet boundar value problem for elliptic equation,in which the nonlinear term contains linear part,parameters and superlinear par-t at infinity.Using the fixed point theorem and method of lower and upper solution,it is proved that the existence of the positive solution when the parameter λ is sufficiently small,and the uniqueness theorem of the solution is proved when the nonlinear term is Lipschitz continuous and the parameterλ is sufficiently small.At the same time,the nonexistence theorem of the solution under certain conditions is proved.As for ap-plications of the theorem,practical examples are given respectively.
fixed point theoremmethod of lower and upper solutionpositive solutionsextreme value principle
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