Existence of Solutions of First-Order Nonlinear Differential Equations by Using Fixed Point Theory
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Existence of Solutions of First-Order Nonlinear Differential Equations by Using Fixed Point Theory
P. D. Bhosale1 S. S. Bellale2, K. B. Alte3, K. L. Chavan4
1Research Scholar, Mathematics Research Centre,
Dayanand Science College, Latur, Maharashtra, India
2Head, Department of Mathematics,
Dayanand Science College, Latur, Maharashtra, India
3PG Student, Mathematics,
Dayanand Science College, Latur, Maharashtra, India
4Asst. Prof., Department of Mathematics,
Dayanand Science College, Latur, Maharashtra, India
Email: pavanrajed80@gmail.com , sidhesh.bellale@gmail.com, ketenalte1234@gmail.com , chavankiran9850@gmail.com.
Abstract: This paper investigates the existence of solutions for first-order nonlinear differential equations through the application of fixed-point theory. By transforming the differential equation into an equivalent integral equation, we construct an appropriate operator on a Banach space of continuous functions. Under suitable assumptions on the nonlinear function involved, we employ classical fixed point results such as the Banach Contraction Principle and the Schauder Fixed Point Theorem to establish the existence of at least one solution. This study not only generalizes classical initial value problems but also highlights the applicability of functional analytic methods to nonlinear differential equations.
Keywords: Banach sapce , fixed point , contraction mapping , Existence of solutions, Integral Equations.
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