A p-Laplacian problem with slightly subcritical regularly varying nonlinearity - Cuesta, Mabel; Pardo, Rosa (Topological Methods in Nonlinear Analysis, 2026)
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 necessarilyasymptotic 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.