n-Kirchhoff type equations with exponential nonlinearities

Abstract

In this article, we study the existence of non-negative solutions of the class of non-local problem of n-Kirchhoff typewhere ⊂ R n is a bounded domain with smooth boundary, n ≥ 2 and f behaves like e |u| n n−1 as |u| → ∞. Moreover, by minimization on the suitable subset of the Nehari manifold, we study the existence and multiplicity of solutions, when f (x, t) is concave near t = 0 and convex as t → ∞.

Polyharmonic Kirchhoff type equations with singular exponential nonlinearities

“…Now we estimate each integral in (19), separately. For arbitrary δ > 0, using the interpolation inequality ab ≤ δa…”

“…The following lemma shows that minimizers for J λ on any of subsets N + λ , N − λ of N λ are usually critical points for J λ . Proof is standard as can be seen in Lemma 3.8 of [19].…”

“…Existence of positive solutions for p-Kirchhoff equations with super critical terms is studied in [12] and [13]. The critical Kirchhoff problem in bounded domains in R 2 with exponential growth nonlinearity is studied in [16] and [19].…”

n-Kirchhoff–Choquard equations with exponential nonlinearity

“…During last few decades, several authors such as in [5,8,11,12,33,34,35] used the Nehari manifold and associated fiber maps approach to study the multiplicity results with polynomial type nonlinearity and sign changing weight functions whereas the n-Laplace problems with exponential type nonlinearity has been addressed in [16,17,18]. In case of Kirchhoff equations with Choquard nonlinearity, we highlight that no result is avalaible in the current literature.…”

“…was studied by Figueiredo and Severo [15]. This result was later extended for the n-Laplace operator by Goyal et al in [16]. It is then a natural question to investigate the existence results for a Kirchhoff equation involving Choquard nonlinearity with exponential growth.…”