A p-Laplacian problem with slightly subcritical regularly varying nonlinearity
DOI:
https://doi.org/10.12775/TMNA.2025.047Keywords
Positive solutions, subcritical nonlinearity, changing sign weight, p-Laplacian, regularly varying functionsAbstract
We study a quasilinear elliptic problem involving the $p$-Laplacian operator and a slightly subcritical nonlinearity with a sign-changing weight. We assume that the slightly subcritical nonlinearity is a regularly varying function at zero and at infinity, which are not necessarily asymptotic to a power at infinity. We state sufficient conditions which guarantee a Palais-Smale condition. We also provide a bifurcation theorem for these nonlinearities, which allow us to state the existence of a bifurcated branch of positive solutions, containing a turning point, and multiplicity of solutions.References
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