Arabian Journal of Mathematics最新文献

The classical symmetry method is often employed to find precise solutions to differential equations. This method has yielded several new symmetry reductions and exact solutions for numerous theoretically and physically relevant partial differential equations. These results, as well as the symmetries of a variety of specific cases of the Fokker–Planck equation, were presented in this study using the classical Lie symmetry approach. New exact solutions to the Fokker–Planck equations are provided for each of the six cases.

We establish a relationship between asymptotic regularity and common stationary points of multivalued mappings on a metric space. As a consequence of our results, we obtain a new common fixed point result for two asymptotically regular single-valued mappings. Our work significantly improves and complements comparable results in the literature.

This paper presents several properties and relations that satisfy the components of a bicomplex holomorphic function. It also exhibits several analogies and differences with the case of analytic functions.

In this paper, we consider a coupled system of hyperbolic and biharmonic-wave equations with variable exponents in the damping and coupling terms. In each equation, the damping term is modulated by a time-dependent coefficient a(t) (or b(t)). First, we state and prove a well-posedness theorem of global weak solutions, by exploiting Galerkin’s method and some compactness arguments. Then, using the multiplier method, we establish the decay rates of the solution energy, under suitable assumptions on the time-dependent coefficients and the range of the variable exponents. We end our work with some illustrative examples.

In this paper, we consider a weighted fractional stochastic integro-differential equation with infinite delay and nonzero initial values involving a Riemann–Liouville fractional derivative of order (1/2<alpha <1). The existence of a mild solution is investigated using fractional calculus, stochastic analysis, and the fixed point theorem. An example is also provided to illustrate the obtained result.

Given a Musielak–Orlicz function (varphi (x,s):Omega times [0,infty )rightarrow {mathbb R}) on a bounded regular domain (Omega subset {mathbb R}^n) and a continuous function (M:[0,infty )rightarrow (0,infty )), we show that the eigenvalue problem for the elliptic Kirchhoff’s equation (-Mleft( int limits _{Omega }varphi (x,|nabla u(x)|)textrm{d}xright) text {div}left( frac{partial varphi }{partial s}(x,|nabla u(x)|)frac{nabla u(x)}{|nabla u(x)|}right) =lambda frac{partial varphi }{partial s}(x,|u(x)|)frac{u(x)}{|u(x)|} ) has infinitely many solutions in the Sobolev space (W_0^{1,varphi }(Omega )). No conditions on (varphi ) are required beyond those that guarantee the compactness of the Sobolev embedding theorem.

Given a nonempty convex subset X of a topological vector space and a real bifunction f defined on (X times X), the associated equilibrium problem consists in finding a point (x_0 in X) such that (f(x_0, y) ge 0), for all (y in X). A standard condition in equilibrium problems is that the values of f to be nonnegative on the diagonal of (X times X). In this paper, we deal with equilibrium problems in which this condition is missing. For this purpose, we will need to consider, besides the function f, another one (g: X times X rightarrow mathbb {R}), the two bifunctions being linked by a certain compatibility condition. Applications to variational inequality problems, quasiequilibrium problems and vector equilibrium problems are given.

Fourth order problems with the differential equation (y^{(4)}-(gy')'=lambda ^2y), where (gin C^1[0,a]) and (a>0), occur in engineering on stability of elastic rods. They occur as well in aeronautics to describe the stability of a flexible missile. Fourth order Birkhoff regular problems with the differential equation (y^{(4)}-(gy')'=lambda ^2y) and eigenvalue dependent boundary conditions are considered. These problems have quadratic operator representations with non-self-adjoint operators. The first four terms of the asymptotics of the eigenvalues of the problems as well as those of the eigenvalues of the problem describing the stability of a flexible missile are evaluated explicitly.

Let N be a (mathbb {Z})-nearalgebra; that is, a left nearring with identity satisfying ( k(nn^{prime })=(kn)n^{prime }=n(kn^{prime })) for all (kin mathbb {Z}), (n,n^{prime }in N) and G be a finite group acting on N. Then the skew group nearring (N*G) of the group G over N is formed. If N is 3-prime ((aNb=0) implies (a=0) or (b=0)), then a nearring of quotients ( Q_{0}(N)) is constructed using semigroup ideals (A_{i}) (a multiplicative closed set (A_{i}subseteq N) such that (A_{i}Nsubseteq A_{i}supseteq NA_{i})) of N and the maps (f_{i}:A_{i}rightarrow N) satisfying ( (na)f_{i}=n(af_{i})), (nin N) and (ain A_{i}). Through (Q_{0}(N)), we discuss the relationships between invariant prime subnearrings (I-primes) of (N*G) and G-invariant prime subnearrings (GI-primes) of N. Particularly we describe all the I-primes (P_{i}) of (N*G) such that each ( P_{i}cap N={0}), a GI-prime of N. As an application, we settle Incomparability and Going Down Problem for N and (N*G) in this situation.

Given a group G and a G-category ({textbf{C}}), we give a condition on a diagram of simplicial sets indexed by ({textbf{C}}) that allows us to define a natural action of G on its homotopy colimit, and some other simplicial sets defined in terms of the diagram. Well-known theorems on homeomorphisms and homotopy equivalences are generalized to equivariant versions.