THE DIFFUSION OF ECONOMIC ACTIVITY ACROSS SPACE: A NEW APPROACH

Dynamic spatial theory has been a fruitful approach to understanding economic phenomena involving time and space. However, several central questions still remain unresolved in this field. The identification of the social optimal allocation of economic activity across time and space is particularly problematic, not been ensured yet in economic growth. Developing a monotone method, we study the optimal solution of the spatial Ramsey model. Under fairly general assumptions, we prove the existence of unique social optimum. Considering a numerical implementation of our algorithm, we study the role played by capital mobility in the neoclassical growth environment. With capital irreversibility and economic openness, space allows for transitional dynamics. Moreover, in this context, capital mobility is beneficial as well in terms of social welfare and inequality. We also consider an application of our method to an extension of the spatial Ramsey model for optimal land-use planning.

Constant Sign Solutions to Linear Fractional Integral Problems and Their Applications to the Monotone Method

This manuscript provides some results concerning the sign of solutions for linear fractional integral equations with constant coefficients. This information is later used to prove the existence of solutions to some nonlinear problems, together with underestimates and overestimates. These results are obtained after applying suitable modifications in the classical process of monotone iterative techniques. Finally, we provide an example where we prove the existence of solutions, and we compute some estimates.

Numerical Results for Linear Sequential Caputo Fractional Boundary Value Problems

The generalized monotone iterative technique for sequential 2 q order Caputo fractional boundary value problems, which is sequential of order q, with mixed boundary conditions have been developed in our earlier paper. We used Green’s function representation form to obtain the linear iterates as well as the existence of the solution of the nonlinear problem. In this work, the numerical simulations for a linear nonhomogeneous sequential Caputo fractional boundary value problem for a few specific nonhomogeneous terms with mixed boundary conditions have been developed. This in turn will be used as a tool to develop the accurate numerical code for the linear nonhomogeneous sequential Caputo fractional boundary value problem for any nonhomogeneous terms with mixed boundary conditions. This numerical result will be essential to solving a nonlinear sequential boundary value problem, which arises from applications of the generalized monotone method.

Ground State Solutions for Quasilinear Schrödinger Equations with Critical Growth and Lower Power Subcritical Perturbation

We study the following generalized quasilinear Schrödinger equation: -(g^{2}(u)\nabla u)+g(u)g^{\prime}(u)|\nabla u|^{2}+V(x)u=h(u),\quad x\in% \mathbb{R}^{N}, where {N\geq 3} , {g\colon\mathbb{R}\rightarrow\mathbb{R}^{+}} is an even differentiable function such that {g^{\prime}(t)\geq 0} for all {t\geq 0} , {h\in C^{1}(\mathbb{R},\mathbb{R})} is a nonlinear function including critical growth and lower power subcritical perturbation, and the potential {V(x)\colon\mathbb{R}^{N}\rightarrow\mathbb{R}} is positive. Since the subcritical perturbation does not satisfy the (AR) condition, the standard variational method cannot be used directly. Combining the change of variables and the monotone method developed by Jeanjean in [L. Jeanjean, On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on {\mathbf{R}}^{N} , Proc. Roy. Soc. Edinburgh Sect. A 129 1999, 4, 787–809], we obtain the existence of positive ground state solutions for the given problem.