Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems with Discontinuous Mappings

Let X, Y be two finite-dimensional topological vector spaces, Z a Hausdorff topological vector space, K C X and D C Z be two nonempty sets, C be a pointed, closed, and convex cone in Y with int C ≠θ Let S ： K → 2^K and T ： K → 2^D be two multivalued mappings, and φ ： K × D × K → Y be a trifunction. In this paper, we consider the generalized vector quasi-equilibrium problem, which is formulated by finding X∈ K and y∈ T（x） such that x∈ E S（x） and φ（x,y, u） （∈/） -int C for all u ∈ S（x）. We establish an existence result in which T is not supposed to have any continuity property. Our results extend and improve the corresponding results of Cubiotti, Yao and Guo.     

An algebraic approach to finding the Fermat–Torricelli point

Using a calculus and an algebraic approach, the Cartesian coordinates of the Fermat–Torricelli point are deduced for triangles with no internal angle greater than 120°. Although in theory, the deduction of these coordinates could be made ‘by hand’, in practice it is very laborious to obtain them without the aid of mathematical computer software, but with human guidance, since there are mathematical artifices not yet incorporated into the software. It is also shown that these coordinates can be conveniently expressed in terms of the side lengths and the area of the triangle. These coordinates are contrasted with the coordinates of a similar point: one whose sum of the squares of the distances to the vertices of an arbitrary triangle is a minimum.     

Existence and Stability of Solutions for Generalized Ky Fan Inequality Problems with Trifunctions

In this paper, an existence theorem for solutions to the generalized Ky Fan Inequality problem is obtained by means of the Kakutani-Fan-Glicksberg fixed-point theorem without imposing the condition that the dual of the ordering cone has a weak* compact base. In addition, the stability of the solution set is shown.     

Existence and Uniqueness of Solutions of Some Cauchy Problems for the Emden–Fowler Equation

Differential Equations - We consider the Cauchy problem for the Emden–Fowler equation $$y^{prime {}prime }-x^ay^{sigma }=0 $$ with parameters $$ain mathbb {R} $$ and $$sigma <0...     

Least-square Solutions of Inverse Problems for Anti-symmetric and Skew-symmetric Matrices

The least-square solutions of inverse problem for anti-symmetric and skew-symmetric matrices are studied. In addition, the problem of using anti-symmetric and skew-symmetric matrices to construct the optimal approximation to a given matrix is discussed, the necessary and sufficient conditions for the problem are derived, and the expression of the solution is provided. A numerical example is given to show the effectiveness of the proposed method.     

Exact Location of the Weighted Fermat–Torricelli Point on Flat Surfaces of Revolution

We find the exact location of the weighted Fermat–Torricelli point of a geodesic triangle on flat surfaces of revolution (circular cylinder and circular cone) in the three dimensional Euclidean space by applying a cosine law of three circular helixes which form a geodesic triangle on a circular cylinder, an explicit solution of the corresponding weighted Fermat–Torricelli point in the dimensional Euclidean space by calculating some lengths of geodesic arcs and angles and by using some lengths of straight lines on a circular cone which connect the vertices of the geodesic triangle with the vertex of the circular cone.     

Multiple Solutions for Systems of Sturm–Liouville Boundary Value Problems

In this paper, the authors discuss the existence of multiple solutions to a class of second-order Sturm–Liouville boundary value systems. Their proofs are based on variational methods and critical point theory.     

Global Existence and Lifespan of Solutions to the Cauchy Problems for the Nonlinear Schrodinger Equations

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Nonlinear Neumann–Transmission Problems for Stokes and Brinkman Equations on Euclidean Lipschitz Domains

The purpose of this paper is to use a layer potential analysis and the Leray–Schauder degree theory to show an existence result for a nonlinear Neumann–transmission problem corresponding to the Stokes and Brinkman operators on Euclidean Lipschitz domains with boundary data in L ^p spaces, Sobolev spaces, and also in Besov spaces.     

Existence of Nonnegative Solutions to Singular Semi-positone Problems

In this paper we study a class of semi-positone singular boundary value problem. With prior bounds estimate and topology degree method, some existence results of nonnegative solution will be shown.     

Wave Interactions and Stability of Riemann Solutions of the Aw–Rascle Model for Generalized Chaplygin Gas

In this paper, we mainly study the interactions of the elementary waves of the Aw–Rascle model for the generalized Chaplygin gas. With the characteristic analysis method, the solutions are obtained constructively when the initial data are three piecewise constant states. Moreover, by studying the limits of the perturbed Riemann solutions as the perturbed parameter \(\varepsilon\) tends to zero, we find that the Riemann solutions are stable for such perturbations on the initial data.     

Infinitely Many Solutions for Systems of Sturm–Liouville Boundary Value Problems

In this paper, the authors obtain the existence of infinitely many classical solutions to the boundary value system with Sturm–Liouville boundary conditions $$\left\{\begin{array}{ll}-(\phi_{p_i}(u_{i}^\prime))^\prime = \lambda F_{u_{i}}(x,u_{1},\ldots,u_{n})h_{i}(u^\prime_i)\quad {\rm in} \, (a,b), \\ \alpha_iu_{i}(a)-\beta_iu^ \prime_{i}(a)=0, \quad \gamma_iu_{i}(b)+\sigma_iu^\prime_{i}(b)=0, \end{array}\quad{i = 1, \ldots , n.} \right.$$ Critical point theory and Ricceri’s variational principle are used in the proofs.     

Existence of Solutions for Singular Boundary Value Problems

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Solitary Wave Solutions and Kink Wave Solutions for a Generalized PC Equation

We present in this paper a generalised PC (GPC) equation which includes several known models. The corresponding traveling wave system is derived and we show that the homoclinic orbits of the traveling wave system correspond to the solitary waves of GPC equation, and the heteroclnic orbits correspond to the kink waves. Under some parameter conditions, the existence of above two types of orbits is demonstrated and the explicit expressions of the two solutions are worked out.     

Asymptotic Behavior of Solutions to the Generalized BBM-Burgers Equation

We investigate the asymptotic behavior of solutions of the initial-boundary value problem for the generalized BBM-Burgers equation u_t f(u)_x=u_(xx) u_(xx) on the half line with the conditions u(0, t)=, u-, u(∞,t)=u_ and, u_-相似文献   

Asymptotic Behavior of Bifurcation Branch of Positive Solutions for Semilinear Sturm–Liouville Problems

We consider the nonlinear eigenvalue problem

Numerical Study of Blow up and Stability of Solutions of Generalized Kadomtsev–Petviashvili Equations

We first review the known mathematical results concerning the Kadomtsev–Petviashvili type equations. Then we perform numerical simulations to analyze various qualitative properties of the equations: blow-up versus long time behavior, stability and instability of solitary waves.