For the mixed local-nonlocal problem with concave-critical nonlinearity, a threshold Lambda_epsilon exists such that positive solutions occur for lambda below it, with at least two solutions for small lambda when epsilon is small enough.
Willem.Minimax theorems, volume 24 ofProgress in Nonlinear Differential Equations and their Applications
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Quasilinear problems with mixed local-nonlocal operator and concave-critical nonlinearities: Multiplicity of positive solutions
For the mixed local-nonlocal problem with concave-critical nonlinearity, a threshold Lambda_epsilon exists such that positive solutions occur for lambda below it, with at least two solutions for small lambda when epsilon is small enough.