The bifurcation diagram for the buckling of a planar elastica under a load λ is made up of a “trivial” branch of unbuckled configurations for all λ and a sequence of branches of buckled configurations that are connected to the trivial branch at pitchfork bifurcation points. We use several perturbation expansions to determine how this diagram perturbs with the addition of a small intrinsic shape...

In this article, we study the bifurcation of positive solutions for the one-dimensional (p, q)-Laplace equation under Dirichlet boundary conditions. We investigate the shape of the bifurcation diagram and prove that there exist five different types of bifurcation diagrams. As a consequence, we prove the existence of multiple positive solutions and show the uniqueness of positive solutions for a...

We study semilinear elliptic equations on general bounded domains with concave semipositone nonlinearities. We prove the existence of the maximal solutions, and describe the global bifurcation diagrams. When a parameter is small, we obtain the exact global bifurcation diagram. We also discuss the related symmetry breaking bifurcation when the domains have certain symmetries.

A transversally driven isotropic ferromagnet being under the influence of a static external and an uniaxial internal anisotropy field is studied. We consider the dissipative Landau-Lifshitz equation as the fundamental equation of motion and treat it in 1 + 1 dimensions. The stability of the spatially homogeneous magnetizations against inhomogeneous perturbations is analyzed. Subsequently the dy...

In the paper we present the qualitative analysis of rolling motion without slipping of a homogeneous round disk on a horisontal plane. The problem was studied by S. A. Chaplygin, P. Appel and D. Korteweg who showed its integrability. The behavior of the point of contact on a plane is investigated and conditions under which its trajectory is finit are obtained. The bifurcation diagrams are const...

The main modes of behavior of a food chain model, composed of logistic prey and Holling type II predator and superpredator, are discussed in this paper. The study is carried out through bifurcation analysis, alternating between a normal form approach and numerical continuation. The two-parameter bifurcation diagram of the model contains Hopf, fold and transcritical bifurcation curves of equilib...

We describe the bifurcation diagrams of almost toric integrable Hamiltonian systems on a four dimensional symplectic manifold M , not necessarily compact. We prove that, under a weak assumption, the connectivity of the fibers of the induced singular Lagrangian fibration M → R can be detected from the bifurcation diagram alone. In this case, it is possible to give a detailed description of the i...