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- W4385890367 abstract "We prove some abstract multiplicity theorems that can be used to obtain multiple nontrivial solutions of critical growth $p$-Laplacian and $(p,q)$-Laplacian type problems. We show that the problems considered here have arbitrarily many solutions for all sufficiently large values of a certain parameter $lambda > 0$. In particular, the number of solutions goes to infinity as $lambda to infty$. Moreover, we give an explicit lower bound on $lambda$ in order to have a given number of solutions. This lower bound is in terms of a sequence of eigenvalues constructed using the ${mathbb Z}_2$-cohomological index. This is a consequence of the fact that our abstract multiplicity results make essential use of the piercing property of the cohomological index, which is not shared by the genus. Our result for the $p$-Laplacian is new even in the semilinear case $p = 2$." @default.
- W4385890367 created "2023-08-17" @default.
- W4385890367 creator A5001888163 @default.
- W4385890367 date "2023-08-15" @default.
- W4385890367 modified "2023-09-27" @default.
- W4385890367 title "Abstract multiplicity theorems and applications to critical growth problems" @default.
- W4385890367 doi "https://doi.org/10.48550/arxiv.2308.07901" @default.
- W4385890367 hasPublicationYear "2023" @default.
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