Existence and Concentration of Positive Solutions for Nonlinear Kirchhoff Type Problems with a General Critical Nonlinearity
Proceedings of the Edinburgh Mathematical Society
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We are concerned with the following Kirchhoff-type equation where M ∈ C(ℝ+, ℝ+), V ∈ C(ℝN, ℝ+) and f(s) is of critical growth. In this paper, we construct a localized bound state solution concentrating at a local minimum of V as ε → 0 under certain conditions on f(s), M and V. In particular, the monotonicity of f(s)/s and the Ambrosetti–Rabinowitz condition are not required.
Kirchhoff equations, Existence and concentration, Critical growth
Costa, D. G.,
do O', J. M.
Existence and Concentration of Positive Solutions for Nonlinear Kirchhoff Type Problems with a General Critical Nonlinearity.
Proceedings of the Edinburgh Mathematical Society, 61(4),