Global existence of solutions to nonlinear Volterra integral equations
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Alexander G. Ramm
Abstract
A new method is given for proving the global existence of the solution to nonlinear Volterra integral equations. A bound on the solution is derived. The results are based on a nonlinear inequality proved by the author earlier.
References
[1] A. G. Ramm, Large-time behavior of solutions to evolution equations, Handbook of Applications of Chaos Theory, Chapman and Hall/CRC, Boca Raton (2016), 183–200. 10.1201/b20232-12Search in Google Scholar
[2] A. G. Ramm and N. S. Hoang, Dynamical Systems Method and Applications. Theoretical Developments and Numerical Examples, Wiley, Hoboken, 2012. 10.1002/9781118199619Search in Google Scholar
[3] P. Zabreiko, Integral Equations, Nauka, Moscow, 1968. Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Two-step collocation methods for two-dimensional Volterra integral equations of the second kind
- Riesz basis of exponential family for a hyperbolic system
- 𝜎-ideals and outer measures on the real line
- Some fractional differential equations involving generalized hypergeometric functions
- Global existence of solutions to nonlinear Volterra integral equations
- Second-order characterization of convex functions and its applications
- On some k-fractional integral inequalities of~Hermite--Hadamard type for twice differentiable generalized beta (r, g)-preinvex functions
- Refinements of the Hermite–Hadamard inequality for co-ordinated convex mappings
- Fractional Ostrowski type inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality
- Some families of sublinear correspondences
- Decay rates for a coupled quasilinear system of nonlinear viscoelastic equations
- A note on the regularity of weak solutions to the coupled 2D Allen–Cahn–Navier–Stokes system
Articles in the same Issue
- Frontmatter
- Two-step collocation methods for two-dimensional Volterra integral equations of the second kind
- Riesz basis of exponential family for a hyperbolic system
- 𝜎-ideals and outer measures on the real line
- Some fractional differential equations involving generalized hypergeometric functions
- Global existence of solutions to nonlinear Volterra integral equations
- Second-order characterization of convex functions and its applications
- On some k-fractional integral inequalities of~Hermite--Hadamard type for twice differentiable generalized beta (r, g)-preinvex functions
- Refinements of the Hermite–Hadamard inequality for co-ordinated convex mappings
- Fractional Ostrowski type inequalities for functions whose certain power of modulus of the first derivatives are pre-quasi-invex via power mean inequality
- Some families of sublinear correspondences
- Decay rates for a coupled quasilinear system of nonlinear viscoelastic equations
- A note on the regularity of weak solutions to the coupled 2D Allen–Cahn–Navier–Stokes system
