We study a nonlocal elliptic equation of $p$-Kirchhoff type involving the critical Sobolev exponent. First we give sufficient conditions for $(\text{PS})$ condition to hold. Then prove some existence and multiplicity results using tools from Morse theory, in particular, notion cohomological local splitting eigenvalues based on Fadell-Rabinowitz index.

Abstract We define a formal algebraic analogue of hypertoric Hitchin systems, whose complex-analytic counterparts were defined by Hausel–Proudfoot. These are completely integrable systems associated to graph $\Gamma $. study the variation Tamagawa number resulting family abelian varieties and show that it is described Kirchhoff polynomial In particular, this allows us compute their $p$-adic vol...

In this paper, I present a modification of the Beylkin inversion operator. This modification accounts for the band-limited nature of the data and makes the role of discontinuities in the sound speed more precise. The inversion presented here partially dispenses with the small-parameter constraint of the Born approximation. This is shown by applying the proposed inversion operator to upward scat...

Igor V. Ovchinnikov, ∗ Wenyuan Li, Yuquan Sun, Robert N. Schwartz, Andrew E. Hudson, Karlheinz Meier, and Kang L. Wang † Department of Electrical Engineering, UCLA, Los Angeles, CA USA LMIB & School of Mathematics and Systems Science, BeiHang University, Beijing 100191, China Department of Anesthesiology and Perioperative Medicine, David Geffen School of Medicine, UCLA, Los Angeles, CA USA Kirc...

Using the mountain pass theorem combined with the Ekeland variational principle, we obtain at least two distinct, non-trivial weak solutions for a class of p(x)-Kirchhoff type equations with combined nonlinearities. We also show that the similar results can be obtained in the case when the domain has cylindrical symmetry.

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with acoustic boundary in a bounded domain in Rn. To stabilize the system, we incorporate separately, the passive viscous damping in the model as like Gannesh C. Gorain [1]. Energy decay rate is obtained by the exponential stability of solutions by using multiplier technique.