Proves relative compactness in the energy space for bounded sequences solving subcritical mixed local-nonlocal problems with exponents approaching 2*, under specific ranges of N and p, yielding infinitely many sign-changing solutions to the critical equation.
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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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Brezis-Nirenberg problems for mixed local-nonlocal operators with superlinear perturbations: compactness and applications
Proves relative compactness in the energy space for bounded sequences solving subcritical mixed local-nonlocal problems with exponents approaching 2*, under specific ranges of N and p, yielding infinitely many sign-changing solutions to the critical equation.