We continue our work (Y. Li, C. Zhao in J Differ Equ 212:208–233, 2005) to study the structure of positive solutions to the equation ε m Δmu − u m−1 + f(u) = 0 with homogeneous Neumann boundary condition in a smooth bounded domain of (N ≥ 2). First, w . . .

We consider the existence of multi-peak solutions to two types of free boundary problems arising in confined plasma and steady vortex pair under conditions on the nonlinearity we believe to be almost optimal. Our results show that the "core" of the so . . .

This paper is contributed to the Cauchy problem

We consider positive solutions of the Dirichlet problem u(x) + λf(u(x)) = 0 on (−1, 1), u(−1 ) =u(1) = 0. depending on a positive parameter λ. Each solution u(x) is an even function, and hence it is uniquely identified by α = u(0). We present a formul . . .

Mathematical models are used to determine if infection wave fronts could occur by traveling geographically in a loop around a region or continent. These infection wave fronts arise by Hopf bifurcation for some spatial models for infectious disease tra . . .

In this paper, we study the following Duffing-type equation: x″+cx′+g(t,x)=h(t), where g(t,x) is a 2π-periodic continuous function in t and concave–convex in x, and h(t) is a small continuous 2π-periodic function. The exact multiplicity and stability . . .

In this paper we will discuss the existence and non-existence of positive solutions to the problem: -Δu = λa(x) f(u), x є Ω | u(x) = 0, x є ᶏΩ (1.1) where Ω will be assumed to be a bounded domain in RN with smooth boundary.

We present exact multiplicity results for the boundary value problems of the type (1.1) u’’+ λf(x, u) = 0 for − L < x < L, u(−L) = u(L) = 0, with the nonlinearity f behaving like a cubic polynomial in u.

The purpose of this paper is to establish the regularity the weak solutions for a nonlinear biharmonic equation.

In this paper, we consider the semilinear elliptic equation [formula] Forp=2N/(N−2), we show that there exists a positive constantμ*>0 such that (∗)μpossesses at least one solution ifμ∈(0, μ*) and no solutions ifμ>μ*. Furthermore, (∗)μpossesses a uniq . . .