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.
Combinedeffectsofconcaveandconvexnonlinearities in some elliptic problems.J
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Existence of weak solutions is shown for a Neumann elliptic problem with discontinuous nonlinearity, plus an estimate for well-posedness under smoother boundary data.
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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.
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Neumann problem with a discontinuous nonlinearity
Existence of weak solutions is shown for a Neumann elliptic problem with discontinuous nonlinearity, plus an estimate for well-posedness under smoother boundary data.