We prove the exact multiplicity of positive boundary blow-up solutions to a semilinear elliptic equation with bistable nonlinearity for the one-dimensional case. We use time-mapping techniques to determine the exact shape of the bifurcation diagram.

We consider the asymptotic analysis and some existence result on blowing up solutions for a semilinear elliptic equation in dimension 2 with nonlinear exponential term, singular sources and Dirichlet boundary condition.

We study a semilinear elliptic equation with an asymptotic linear nonlinearity. Exact multiplicity of solutions are obtained under various conditions on the nonlinearity and the spectrum set. Our method combines a bifurcation approach and Leray–Schauder degree theory.

A semilinear elliptic equation with generalized cubic nonlinearity is studied. Global bifurcation diagrams and the existence of multiple solutions are obtained and in certain cases, exact multiplicity is proved.

We prove nonexistence of nonconstant global minimizers with limit at infinity of the semilinear elliptic equation −∆u = f(u) in the whole R , where f ∈ C(R) is a general nonlinearity and N ≥ 1 is any dimension. As a corollary of this result, we establish nonexistence of nonconstant bounded radial global minimizers of the previous equation.

In this paper we extend the idea of interpolated coefficients for semilinear problems to the finite volume element method based on rectangular partition. At first we introduce bilinear finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. Next we derive convergence estimate in H 1-norm and superconvergence of derivative. Finall...

Abstract. We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. The problem arises from the aim to optimize the temperature gradient within crystal growth by the physical vapor transport (PVT) method. Based on a minimum...

Abstract. We consider a system of a semilinear hyperbolic functional differential equation (where the lower order terms contain functional dependence on the unknown functions) with initial and boundary conditions and a quasilinear elliptic functional differential equation (containing t as a parameter) with boundary conditions. Existence of solutions for t ∈ (0, T ) will be shown and some exampl...