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- W1965338972 abstract "In this paper, we study the existence, multiplicity and concentration of positive solutions for a class of quasilinear problems where —Δ p is the p -Laplacian operator for is a small parameter, f(u) is a superlinear and subcritical nonlinearity that is continuous in u . Using a variational method, we first prove that for sufficiently small ε > 0 the system has a positive ground state solution u ε with some concentration phenomena as ε → 0. Then, by the minimax theorems and Ljusternik–Schnirelmann theory, we investigate the relation between the number of positive solutions and the topology of the set of the global minima of the potentials. Finally, we obtain some sufficient conditions for the non-existence of ground state solutions." @default.
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- W1965338972 date "2015-04-01" @default.
- W1965338972 modified "2023-09-27" @default.
- W1965338972 title "Positive solutions for a class of quasilinear problems with critical growth in ℝN" @default.
- W1965338972 doi "https://doi.org/10.1017/s0308210513001492" @default.
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