Collocation semi-discretizations based on Chan's SBP operator are equivalent to DG semi-discretizations on the same quadrature, with extraneous modes remaining zero.
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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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A collocation scheme that is equivalent to discontinuous Galerkin discretizations
Collocation semi-discretizations based on Chan's SBP operator are equivalent to DG semi-discretizations on the same quadrature, with extraneous modes remaining zero.
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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.