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Abstract In this paper, we study the existence of sign-changing (nodal) and nontrivial solutions for the nonlinear Kirchhoff-type equation { − ( a + b ∫ Ω | ∇ u… Click to show full abstract
Abstract In this paper, we study the existence of sign-changing (nodal) and nontrivial solutions for the nonlinear Kirchhoff-type equation { − ( a + b ∫ Ω | ∇ u | 2 d x ) Δ u = α u + β u 3 in Ω , u = 0 on ∂ Ω , where α , β ∈ R are two real parameters. With the help of nodal Nehari set, we first provide a description of a two-dimensional set in the ( α , β ) plane, which corresponds to the nonexistence and existence of sign-changing solutions for the above Kirchhoff-type equation. And then, we establish the existence result of nontrivial solutions via the minimax methods.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2020
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