Abstract
Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations
Highlights
The study of heteroclinic solutions for second-order ordinary differential equations can be applied to various biological, physical, and chemical models, for instance, phase-transition, M
We mention that in [29], by means of a suitable fixed point technique, Malaguti and Marcelli proved the existence of a one-parameter family of solutions of the nonautonomous problem u = h(t, u, u ) on R, u(−∞) = 0, u(∞) = 1, where h : R3 → R is continuous, and h(t, u, v)/v is monotone nondecreasing in v for each (t, u) ∈ R × (0, 1)
Inspired by the above works and [19, 39], the main aim of the present paper is to establish the new results on the existence, uniqueness, and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations y = f (x, y, y ) on R
Summary
Inspired by the above works and [19, 39], the main aim of the present paper is to establish the new results on the existence, uniqueness, and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations y = f (x, y, y ) on R (1.1). Our Theorem 3.4 for problem (1.2) complements theorem 4.2 in [7]
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