4 papers
Singular solutions and bifurcation diagram of semilinear elliptic equations with general nonlinearity in two dimensions
Hiroaki Kikuchi, Kenta Kumagai
In this paper, we investigate semilinear elliptic equations with general exponential-type nonlinearities in two dimensions. For such nonlinearities, we establish two main results.…
Classification of bifurcation structure for semilinear elliptic equations in a ball
Kenta Kumagai
We consider the Gelfand problem with Sobolev supercritical nonlinearities in the unit ball. In the case where is a power type nonlinearity or the exponential nonlinearity,…
Uniformly boundedness of finite Morse index solutions to semilinear elliptic equations with rapidly growing nonlinearities in two dimensions
Kenta Kumagai
We consider the Gelfand problem with rapidly growing nonlinearities in the two-dimensional bounded strictly convex domains. In this paper, we prove the uniformly boundedness of fin…
Bifurcation diagrams for semilinear elliptic equations with singular weights in two dimensions
Kenta Kumagai
We consider the bifurcation diagram of radial solutions for the Gelfand problem with a positive radially symmetric weight in the unit ball. We deal with the exponential nonlinearit…