Positive solutions for nonlinear nonhomogeneous parametric equations (Q526095)

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scientific article; zbMATH DE number 6712674
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Positive solutions for nonlinear nonhomogeneous parametric equations
scientific article; zbMATH DE number 6712674

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    Positive solutions for nonlinear nonhomogeneous parametric equations (English)
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    8 May 2017
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    This paper deals with the study of a nonlinear parametric elliptic problem with Dirichlet boundary condition. A feature of this paper is the presence of a nonhomogeneous differential operator, which generalizes the standard cases corresponding to the \(p\)-Laplace operator, the \((p,q)\)-Laplacian and the generalized \(p\)-mean curvature operator. Combining variational and topological arguments, the authors establish a bifurcation-type theorem that describes the dependence of positive solutions on the parameter.
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    nonlinear regularity
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    mountain pass theorem
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    bifurcation-type theorem
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    strong comparison principle
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    nonhomogeneous differential operator
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    positive solutions
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