相关论文: Bifurcation Curve Diagrams for a Diffusive General…
In this paper, we shall establish the unilateral global bifurcation result for a class of fourth-order eigenvalue problems with sign-changing weight. Under some natural hypotheses on perturbation function, we show that $(\mu_k^\nu,0)$ is a…
A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of…
We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite…
We discuss the existence of multiple positive solutions leading to the occurrence of an S-shaped bifurcation curve to the equations of the form $$ -\Delta_p u= f(\mu,\lambda, u)~ \mbox{in} ~\Omega \subset \mathbb{R}^N $$ where $\Delta_p$ is…
The global bifurcation diagrams for two different one-parametric perturbations ($+\lambda x$ and $+\lambda x^2$) of a dissipative scalar nonautonomous ordinary differential equation $x'=f(t,x)$ are described assuming that 0 is a constant…
We prove global asymptotic bifurcation for a very general class of asymptotically linear Schr\"odinger equations \begin{equation}\label{1} \{{array}{lr} \D u + f(x,u)u = \lam u \quad \text{in} \ {\mathbb R}^N, u \in H^1({\mathbb…
Global solution curve and exact multiplicity of positive solutions for a class of fourth-order beam equations with clamped boundary conditions are derived. The results extend atheorem of P. Korman (2004) by allowing the presence of a…
A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is…
We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation…
We prove the existence of a global bifurcation branch of $2\pi$-periodic, smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of solutions in the global branch contains a sequence which converges uniformly…
We consider a simplified version of the Budyko diffusive energy balance climate model. We obtain the exact number of monotone stationary solutions of the associated discontinuous nonlinear elliptic with absorption. We show that the…
A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered. The results on existence and uniqueness of solutions of these problems as…
We study multiplicity of constant scalar curvature metrics in products of a compact closed manifold and a compact manifold with boundary using equivariant bifurcation theory.
We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray…
We present numerical solution of the chlorine dioxide-iodine-malonic acid reaction-diffusion system in two dimensions in a boundary-fed system using a realistic model. The bifurcation diagram for the transition from non-symmetry breaking…
We shall study the solvability of pseudodifferential operators which are not of principal type. The operator will have real principal symbol and we shall consider the limits of bicharacteristics at the set where the principal symbol…
Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…
We consider transversely modulated fronts in a directionally quenched Cahn-Hilliard equation, posed on a two-dimensional infinite channel, with both parameter and source-term type heterogeneities. Such quenching heterogeneities travel…
Nonnegative measures that are solutions to a transport equation with continuous coefficients have been widely studied. Because of the low regularity of the associated vector field, there is no natural flow since nonuniqueness of integral…
We give a comprehensive analysis of the Euler-Jacobi problem of motion in the field of two fixed centers with arbitrary relative strength and for positive values of the energy. These systems represent nontrivial examples of integrable…