Abstract In this paper, we study a class of ( p , q )-Schrödinger–Kirchhoff type equations involving continuous positive potential satisfying del Pino–Felmer conditions and nonlinearity with subcritical growth at infinity. By applying variational methods, penalization techniques Lusternik–Schnirelman category theory, relate the number solutions topology set where attains its minimum values.

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.

We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential V . Under suitable assumptions on V , using the monotonicity trick and the profile decomposition, we prove the existence of ground states. In particular, the nonlinearity does not satisfy the Ambrosetti-Rabinowitz type condition or monotonicity assumptions.

We show under mild assumptions that a composition of internally well-posed, impedance passive (or conservative) boundary control systems through Kirchhoff type connections is also an internally well-posed, impedance passive (resp., conservative) boundary control system. The proof is based on results of [21]. We also present an example of such composition involving Webster’s equation on a Y-shap...

We compute explicitly the solution of the heat equation on a weighted graph 0 whose edges are identified with copies of the segment [0, 1] with the condition that the sum of the weighted normal exterior derivatives is 0 at every node (Kirchhoff type condition).