Lyapunov type inequalities for second-order forced dynamic equations with mixed nonlinearities on time scales

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Atıf İçin Kopyala

Agarwal R. P., ÇETİN E., Ozbekler A.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, cilt.111, sa.1, ss.231-246, 2017 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 111 Sayı: 1
• Basım Tarihi: 2017
• Doi Numarası: 10.1007/s13398-016-0290-6
• Dergi Adı: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.231-246
• Ankara Üniversitesi Adresli: Hayır

Özet

In this paper, we present some newHartman and Lyapunov inequalities for second-order forced dynamic equations on time scales T with mixed nonlinearities: x(Delta Delta)(t) + Sigma(n)(k=1) qk (t)vertical bar x(sigma) (t)vertical bar (alpha k-1) x(sigma) (t) = f (t); t is an element of [t(0), infinity)(T), where the nonlinearities satisfy 0 < alpha(1) < ... < alpha(m) < 1 < alpha(m+1) < ... < alpha(n) < 2. No sign restrictions are imposed on the potentials qk, k = 1, 2, ... , n, and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature.