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NONLINEAR SINGULAR EIGENVALUE PROBLEMS
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DOI：10.1007/s10473-026-0321-0.png)
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Abstract
En 中文
We study a nonlinear eigenvalue problem driven by a general nonhomogeneousdifferential operator, involving a reaction term that is singular at x = 0 and becomes superlinear as x -> + infinity. Unlike the usual case in the literature, the singular term and theperturbation are not decoupled. By using variational methods in combination with trun-cation and comparison techniques, we establish a global existence and multiplicity theoremwith respect to the parameter (eigenvalue) lambda > 0. Additionally, we demonstrate the existenceof a minimal positive solution u(lambda )(& lowast;)and investigate the continuity and monotonicity propertiesof the map lambda -> u(lambda)(& lowast;)
Keywords:
singular and superlinear reaction
nonlinear regularity
nonlinear maximum principle
truncations and comparisons
minimal positive solutions
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1.1
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97
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