Abstract
In this work, we are mainly concerned with the existence of stationary solutions for the generalized Kadomtsev-Petviashvili equation in bounded domain in R n 8
Highlights
We shall investigate the stationary solutions for the generalized Kadomtsev-Petviashvili equation in bounded domain in Rn
We say that φ satisfies the PalaisSmale condition ((PS) condition for short) if for every sequence {um} ⊂ X such that φ(um) is bounded and φ′(um) → 0 as m → ∞, there exists a subsequence of {um} which is convergent in X
We say that φ satisfies (PS)c condition if the existence of a sequence {um} ⊂ X such that φ(um) → c and φ′(um) → 0 as m → ∞ lead to c is a critical value of φ
Summary
Yn−1) ∈ R+ × R × Rn−1, n ≥ 2, Dx−1 and ∆y are as in (1.1). We say that φ satisfies (PS)c condition if the existence of a sequence {um} ⊂ X such that φ(um) → c and φ′(um) → 0 as m → ∞ lead to c is a critical value of φ. Lemma 2.3(see [28, Theorem 1.2]) Suppose X is a reflexive Banach space with norm · , and let M ⊂ X be a weakly closed subset of X.
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