This report contains a survey on recent results concerning solutions of the second order nonlinear differential equation $x'' + a(t)|x|^\gamma \operatorname{sgn} x = 0$, $\gamma > 0$, where $a(t)$ is continuous and nonnegative. Specifically, the questions concerning continuability, boundedness, stability, oscillation, asymptotic growth and boundary value problems are discussed. An extensive list of related references is also included.

On the Generalized Emden–Fowler Equation

We develop a dynamic asset-pricing model of cryptocurrencies/tokens that allow users to conduct peer-to-peer transactions on digital platforms. The equilibrium value of tokens is determined by aggregating heterogeneous users' transactional demand rather than discounting cashflows as in standard valuation models. Endogenous platform adoption builds upon user network externality and exhibits an S-curve — it starts slow, becomes volatile, and eventually tapers off. Introducing tokens lowers users' transaction costs on the platform by allowing users to capitalize on platform growth. The resulting intertemporal feedback between user adoption and token price accelerates adoption and dampens user-base volatility.

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Tokenomics: Dynamic Adoption and Valuation

https://www.kau.edu.sa/Files/130/Researches/60166_30987.pdf

On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order

Boundary value problems for higher order differential equations

Subfunctions and second-order ordinary differential inequalities

Existence and uniqueness of solutions of boundary value problems for third order differential equations

Comparison theorems for nonlinear differential equations

The proof of the sufficiency of the differential inequality is based on [1, Lemma 1, p. 565 ] but the proof of the lemma does not appear to be correct. After some preliminary results in ?1, we give in ?2 a proof of Theorem 1 by a quite different method. Also in ?2 a modification of Theorem 1 is given in which the assumption of the solvability of the boundary value problem is replaced by a monotoneity condition.

/pdf/on-second-order-differential-inequalities-3axs70t9jo.pdf

Lloyd K Jackson

Papers

Subfunctions and second-order ordinary differential inequalities

Existence and uniqueness of solutions of boundary value problems for third order differential equations

Comparison theorems for nonlinear differential equations

On second order differential inequalities

Existence and uniqueness of solutions of boundary value problems for Lipschitz equations