We study false vacuum decays catalysed by magnetic monopoles which act as tunnelling sites with exponentially enhanced decay rates. The field profiles describing the do not have typically assumed $O(3)/O(4)$ symmetry, thus requiring an extension of usual rate calculation. To numerically determine saddle point solutions describe process we use a new algorithm based on mountain pass theorem. This...

in the present paper, the deformation zone of the ecae (equal channel angular extrusion) process was investigated using the upper bound theorem. for this purpose, the shape of the streamlines in the deformation zone was assumed to be cubic bezier curves. then, the force required for the ecae process was optimized with regard to the parameters defining the shape of streamlines by the upper bound...

Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. We initiate the corresponding study of higher critical points by considering a superlinear free boundary problem related to plasma confinement. The associated energy functional is nondifferentiable, and therefore standard variational methods cannot be used directly to prove...

We study a Hamiltonian system that has a superquadratic potential and is asymptotic to an autonomous system. In particular, we show the existence of a nontrivial solution homoclinic to zero. Many results of this type rely on a convexity condition on the nonlinearity, which makes the problem resemble in some sense the special case of homogeneous (power) nonlinearity. This paper replaces that con...

This article initiates the study of nonlinear elliptic partial difference equations (PdE) on graphs. We seek solutions u : V → R to the semilinear elliptic difference equation −Lu + f(u) = 0 on a graph G = (V,E), where L is the (negative) Laplacian on the graph G. We extend techniques used to prove existence theorems and derive numerical algorithms for the partial differential equation (PDE) ∆u...

ed sign out of two iconically derived signs. This is furthered by Japanese kokuji, invented to represent Japanese words using compound Chinese characters. Other SS combinations are 働 meaning EFFORT, made from PERSON, 人 , and MOVE, 動, and the visually iconic 峠 meaning MOUNTAIN PASS, made by combining mountain, 山, with UP, 上, and DOWN, 下, which create a visual “pass” between them (all examples fr...

Abstract In this article, we study the existence of multiple solutions to a generalized p ( ⋅ ) p\left(\cdot ) -Laplace equation with two parameters involving critical growth. More precisely, give sufficient “local” conditions, which mean that growths between ma...

This paper is concerned with the following Euler-Lagrange system \[ \begin{cases} \frac{d}{dt} \mathcal{L}_v(t,u(t),\dot{u}(t)) = \mathcal{L}_x(t,u(t),\dot{u}(t)) \quad \textrm{for a.e. $t \in [-T,T]$}, \\ u(-T) u(T), \mathcal{L}_v(-T,u(-T),\dot{u}(-T)) \mathcal{L}_v(T,u(T),\dot{u}(T)), \end{cases} \] where Lagrangian given by $\mathcal{L} F(t,x,v) + V(t,x) \langle f(t), x \rangle$, growth cond...