Chung-Cheng Kuo

Additive perturbations of local C-semigroups

Abstract In this paper, we apply the contraction mapping theorem to establish some bounded and unbounded additive perturbation theorems concerning local C-semigroups. Some growth conditions of perturbations of local C-semigroups are also established.

On the solvability of a nonlinear second-order elliptic equation at resonance II

We study the existence of solutions of the Neumann problem for semilinear second-order elliptic equations at resonance in which the nonlinear terms may grow superlinearly in one of the directions u oo and u -oo , and sublinearly in the other. Solvability results are obtained under assulmptions either with or without a Landesman-Lazer condition. The proofs are based on degree-theoretic arguments.

Solvability of a nonlinear two-point boundary value problem at resonance II ☆

Abstract In this article we apply the Leray–Schauder continuation method to obtain existence theorems of solutions for (i) u″+u+g(x,u)=h in (0,π), u(0)=u(π)=0 in which the nonlinearity g grow superlinearly in u in one of directions u→∞ and u→−∞, and may grow sublinearly in the other, and for (ii) −u″−u+g(x,u)=h in (0,π), u(0)=u(π)=0 in which the nonlinearity g has no growth restriction in u as |u|→∞. The L1(0,π) function h may satisfy ∫ 0 π g β − (x) sin x d x ∫ 0 π h(x) sin x d x=0 ∫ 0 π g α + (x) sin x d x , where α, β⩾0 , g α + (x)= lim inf u→∞ g(x,u)|u| α , and g β − (x)= lim sup u→−∞ g(x,u)|u| β .

Multiplicative perturbations of local α-times integrated C-semigroups

Abstract We establish some left and right multiplicative perturbations of a local α-times integrated C -semigroup S (ċ) on a complex Banach space X with non-densely defined generator, which can be applied to obtain some additive perturbation results concerning S (ċ). Some growth conditions of the perturbations of S (ċ) are also established.