Abstract
We study the multiplicity and concentration behaviour of positive solutions for a quasi-linear Choquard equationwhere Δp is the p-Laplacian operator, 1 < p < N, V is a continuous real function on ℝN, 0 < μ < N, F(s) is the primitive function of f(s), ε is a positive parameter and * represents the convolution between two functions. The question of the existence of semiclassical solutions for the semilinear case p = 2 has recently been posed by Ambrosetti and Malchiodi. We suppose that the potential satisfies the condition introduced by del Pino and Felmer, i.e.V has a local minimum. We prove the existence, multiplicity and concentration of solutions for the equation by the penalization method and Lyusternik–Schnirelmann theory and even show novel results for the semilinear case p = 2.
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Schedule a callMore From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
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