LYAPUNOV TYPE INEQUALITIES FOR nTH ORDER FORCED DIFFERENTIAL EQUATIONS WITH MIXED NONLINEARITIES

Agarwal R. P., Ozbekler A.

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, cilt.15, sa.6, ss.2281-2300, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 6
  • Basım Tarihi: 2016
  • Doi Numarası: 10.3934/cpaa.2016037
  • Dergi Adı: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2281-2300
  • Ankara Üniversitesi Adresli: Hayır

Özet

In the case of oscillatory potentials, we present Lyapunov type inequalities for nth order forced differential equations of the form x((n))(t) + Sigma(m)(j=1) qj (t)vertical bar x(t)vertical bar(alpha j-1)x(t)= f(t) satisfying the boundary conditions x(a(i)) = x(1)(a(i)) = x(11)(ai) = center dot center dot center dot = x((ki))(ai) = 0; i = 1, 2,..., r, where a(1) < a(2) < ... < a(r), 0 <= k(i) and Sigma(r)(j=1) k(j) + r = n: r >= 2. No sign restriction is imposed on the forcing term and the nonlinearities satisfy 0 < alpha(l) < ... < alpha a(j) < 1 < alpha a(j+1) < ... < alpha(m) < 2. The obtained inequalities generalize and compliment the existing results in the literature.