Régularité de la solution d'un problème à dérivée oblique, pour l'opérateur de Laplace, dans un polygone plan
The aim of this paper is to study the existence of solutions to a boundary value problem associated to a nonlinear fractional differential equation where the nonlinear term depends on a fractional derivative of lower order posed on the half-line. An appropriate compactness criterion and suitable Banach spaces are used and so a fixed point theorem is applied to obtain fixed points which are solutions of our problem.
Si considerano equazioni di Ginzburg-Landau complesse del tipo in dove è polinomio di grado a coefficienti complessi e è un numero complesso con parte reale positiva . Nell'ipotesi che la parte reale del coefficiente del termine di grado massimo sia positiva, si dimostra l'esistenza e la regolarità di una soluzione globale nel caso , dove dipende da e .
In this paper, we consider the following boundary value problem where and is a continuous function, , are respectively the left and right fractional Riemann–Liouville derivatives and we prove the existence of at least one solution for this problem.
We use the genus theory to prove the existence and multiplicity of solutions for the fractional -Kirchhoff problem where is an open bounded smooth domain of , , with fixed, , is a numerical parameter, and are continuous functions.
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