Integral inequalities of Gronwall-Bellman-Bihari type and asymptotic behavior of certain second order nonlinear differential equations

DOI10.1016/0022-247X(85)90014-9zbMath0586.26008OpenAlexW2007232890MaRDI QIDQ1071882

Fozi M. Dannan

Publication date: 1985

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(85)90014-9

zbMATH Keywords

asymptotic behaviorsecond order differential equationintegral inequalities of the Gronwall-Bellman-Bihari type

Mathematics Subject Classification ID

Growth and boundedness of solutions to ordinary differential equations (34C11) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (30)

Lipschitz stability of nonlinear systems of differential equations ⋮ Nonlinear Gronwall-Bellman type inequalities and their applications ⋮ Some integral inequalities in \(N\) independent variables ⋮ Submultiplicative and subadditive functions and integral inequalities of Bellman-Bihari type ⋮ \(h\)-stability for linear dynamic equations on time scales ⋮ Asymptotic integration of a system resulting from the perturbation of an h-system ⋮ Asymptotic integration of nonlinear \(\phi\)-Laplacian differential equations ⋮ Some new nonlinear retarded sum-difference inequalities with applications ⋮ Global existence of solutions for perturbed differential equations ⋮ On the asymptotic behavior of certain second order nonlinear differential equations ⋮ Some generalized nonlinear retarded integral inequalities with applications ⋮ On the asymptotic integration of nonlinear differential equations ⋮ Blow-up and global solvability of the Cauchy problem for a pseudohyperbolic equation related to the generalized Boussinesq equation ⋮ On the asymptotic behavior of solutions of higher-order nonlinear differential equations ⋮ Cauchy problem for the equation of torsional vibrations of a rod in a viscoelastic medium ⋮ The Cauchy problem for the nonlinear long longitudinal waves equation in a viscoelastic rod ⋮ On a Bellman-Bihari type integral inequality with delay ⋮ On a generalized retarded integral inequality with two variables ⋮ A fractional Bihari inequality and some applications to fractional differential equations and stochastic equations ⋮ Some new nonlinear Gronwall-Bellman-type integral inequalities and applications to BVPs ⋮ Asymptotic behavior of solutions for a class of fractional integro-differential equations ⋮ Global existence of solutions with prescribed asymptotic behavior for second-order nonlinear differential equations ⋮ Asymptotic to polynomials solutions for nonlinear differential equations ⋮ Generalization of a retarded Gronwall-like inequality and its applications ⋮ A generalized retarded Gronwall-like inequality in two variables and applications to BVP ⋮ Asymptotic behavior of solutions of fractional differential equations with Hadamard fractional derivatives ⋮ ASYMPTOTIC INTEGRATION OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRODIFFERENTIAL RIGHT-HAND SIDE ⋮ ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS ⋮ Lipschitz stability of nonlinear systems of differential equations. II: Lyapunov functions ⋮ Bihari type inequalities with multiple integral and delay

Cites Work

• On some integral inequalities similar to Bellman-Bihari inequalities
• On some generalizations o f Bellman's lemma
• On some discrete inequalities of the Bellman-Bihari type
• A note on Gronwall-Bellman inequality
• Some generalizations of Bellman-Bihari integral inequalities
• On a generalization of the Gronwall-Bellman lemma in partially ordered Banach spaces
• A generalization of a lemma of bellman and its application to uniqueness problems of differential equations
• More Generalised Discrete Gronwall Inequalities
• The Asymptotic Behavior of a Class of Nonlinear Differential Equations of Second Order
• More About Quotients of Monotone Functions
• The Asymptotic Behavior of a Class of Nonlinear Differential Equations
• On the Asymptotic Behavior of Solutions of Second Order Linear Differential Equations
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