Application of Lipschitz viscosity solutions for higher-order partial differential equations containing the special Lagrangian operator SeyedMohammadErfan Hosseini, Somayeh Saiedinezhad Tamkang Journal of Mathematics, 2025 Using the Lipschitz continuity of a class of viscosity solutions, we find a kind of viscosity solution for some higher-order partial differential equations containing the special Lagrangian operator. Additionally, we extend this analysis to equations that simultaneously contain the special Lagrangian and some other operators including Laplacian.
A System of High-Order Fractional Differential Equations with Integral Boundary Conditions M. Sangi, S. Saiedinezhad, M. B. Ghaemi Journal of Nonlinear Mathematical Physics, 2023 The existence of a solution for a system of two nonlinear high-order fractional differential equations including the Atangana-Baleanu-Caputo derivative with integral boundary conditions, is proved. Simultaneously, we discuss the existence of a solution by applying the Schauder fixed point theorem and a generalized Darbo fixed point theorem, which involves the concept of measure of noncompactness. The paper also contains some examples that illustrate the application of the main result.
A series of refinements on the young and reverse young inequalities through a recursive algorithm S. Saiedinezhad International Journal of Nonlinear Analysis and Applications, 2020 In this article, we present a recursive algorithm to obtain a series of refinements of the classical Young inequality. These inequalities approach to equalities when the number of the iteration in the recursive algorithm tends to infinity. Also these refinements applied to establish some improved reverse Young and matrix Young inequalities with Hilbert- Schmidt norm.
Existence and asymptotically stable solution of a Hammerstein type integral equation in a Holder space Somayeh Saiedinezhad Bulletin of the Belgian Mathematical Society Simon Stevin, 2018 The following nonlinear quadratic integral equation of Hammerstein type is studied. $$x(t)=p(t)+x(t)\int_0^{q(t)} H(t,\tau,x(\tau)){\rm d}\tau.$$ The methodology relies on the measure of noncompactness in the space of functions with tempered increments, namely the space of $\alpha$-Hölder continuous functions. The results follow from the Darbo fixed point theorem. Some examples are included to show the applicability of the main results.
Existence of solutions to biharmonic equations with sign-changing coefficients Electronic Journal of Differential Equations, 2018
Multiplicity results for a nonlinear robin problem with variable exponent Journal of Nonlinear and Convex Analysis, 2016
The fibering map approach to a quasilinear degenerate p(X)-laplacian equation Bulletin of the Iranian Mathematical Society, 2015
The existence of weak solution for degenerate Σ Δpi(x)-equation Journal of Computational Analysis and Applications, 2011
Preference of monotonicity method to variational method in some classes of P(X)-laplacian problems Australian Journal of Basic and Applied Sciences, 2011
