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Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses

  • Jan Tomeček EMAIL logo
Published/Copyright: April 28, 2017
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 67 Issue 2

Abstract

The paper deals with the boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses of the form

ϕ(z′(t))′=f(t,z(t),z′(t)) for a.e. t∈[0,T]⊂R,Δz′(t)=M(z(t),z′(t−)),t=γ(z(t)),z(0)=z(T)=0.

Here, T > 0, ϕ : ℝ → ℝ is an increasing homeomorphism, ϕ(ℝ) = ℝ, ϕ(0) = 0, f : [0, T] × ℝ2 → ℝ satisfies Carathéodory conditions, M : ℝ → ℝ is continuous and γ : ℝ → (0, T) is continuous, Δ z′(t) = z′(t+) − z′(t−). Sufficient conditions for the existence of at least one solution to this problem having no pulsation behaviour are provided.

MSC 2010: Primary 34B37
Keywords: ϕ-Laplacian; state-dependent impulse; ordinary differential equation; second order; Dirichlet boundary value problem; existence result

(Communicated by Michal Fečkan)

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Received: 2014-12-6
Accepted: 2015-5-16
Published Online: 2017-4-28
Published in Print: 2017-4-25

© 2017 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2016-0283
Keywords for this article
ϕ-Laplacian; state-dependent impulse; ordinary differential equation; second order; Dirichlet boundary value problem; existence result

Articles in the same Issue

  2. 10.1515/ms-2015-0200
  4. Zero-divisor graphs of lower dismantlable lattices I
  6. Some results on the intersection graph of submodules of a module
  8. Class number parities of compositum of quadratic function fields
  10. Examples of beurling prime systems
  12. Connection between multiplication theorem for Bernoulli polynomials and first factor hp−
  14. On permutational invariance of the metric discrepancy results
  16. Evaluation of sums containing triple aerated generalized Fibonomial coefficients
  18. Linear algebraic proof of Wigner theorem and its consequences
  20. A note on groups with finite conjugacy classes of subnormal subgroups
  22. Groups with the same complex group algebras as some extensions of psl(2, pn)
  24. Klee-Phelps convex groupoids
  26. On analytic functions with generalized bounded Mocanu variation in conic domain with complex order
  28. Weak interpolation for the lipschitz class
  30. Generalized Padé approximants for plane condenser and distribution of points
  32. Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
  34. Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential
  36. Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem
  38. Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses
  40. On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term
  42. Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential
  44. Semi-equivelar maps on the torus and the Klein bottle with few vertices
  46. A problem considered by Friedlander & Iwaniec and the discrete Hardy-Littlewood method
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