This paper deals with multiplicity results for nonlinear elastic equations of the typewheregi[0,1] X R R satisfies Caratheodory condition L2[0,1]. The solvability of this problem has been studied by several authors, b...This paper deals with multiplicity results for nonlinear elastic equations of the typewheregi[0,1] X R R satisfies Caratheodory condition L2[0,1]. The solvability of this problem has been studied by several authors, but there isn't any multiplicity result until now to the author's knowledge. By combining the Lyapunov-Schmidt procedure with the technique of connected set, we establish several multiplicity results under suitable condition.展开更多
This paper deals with multiplicity results for nonlinear elastic equations of the type wheree∈L￣2(0,1),g:[0,1]×R×R→R is a bounded contimuous function.and the pair(α,β)satisfiesand
This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and ...This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.展开更多
We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem y″″=λa（x）f（y）,0〈x〈1,y（0）=y（1）=y″（0）=y″（1）=0where λ is a positive...We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem y″″=λa（x）f（y）,0〈x〈1,y（0）=y（1）=y″（0）=y″（1）=0where λ is a positive parameter, a ∈ C（[0, 1], （0, ∞）, f ∈C（R,R） satisfies f（u）u 〉 0 for all u ≠ 0. We give conditions on the ratio f（s）/s, at infinity and zero, that guarantee the existence of nodal solutions.The proof of our main results is based upon bifurcation techniques.展开更多
The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation o...The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation on a compact interval[a,b] R{-u＇＇=（λf（x,u）＋g（u））h（u＇）,in（a,b）,u（a）=u（b）=0under ppropriate hypotheses.We exhibit the existence of at least three（weak）solutions and,and the results are illustrated by examples.展开更多
文摘This paper deals with multiplicity results for nonlinear elastic equations of the typewheregi[0,1] X R R satisfies Caratheodory condition L2[0,1]. The solvability of this problem has been studied by several authors, but there isn't any multiplicity result until now to the author's knowledge. By combining the Lyapunov-Schmidt procedure with the technique of connected set, we establish several multiplicity results under suitable condition.
文摘This paper deals with multiplicity results for nonlinear elastic equations of the type wheree∈L￣2(0,1),g:[0,1]×R×R→R is a bounded contimuous function.and the pair(α,β)satisfiesand
基金supported by the NNSF of China(10671064)the second author was supported by the Australian Research Council's Discovery Projects(DP0450752)
文摘This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.
基金the NSFC (No.10671158)the NSF of Gansu Province (No.3ZS051-A25-016)+3 种基金NWNUKJCXGC-03-17the Spring-Sun Program (No.Z2004-1-62033)SRFDP (No.20060736001)the SRF for ROCS,SEM (2006[311])
文摘We are concerned with determining the values of λ, for which there exist nodal solutions of the fourth-order boundary value problem y″″=λa（x）f（y）,0〈x〈1,y（0）=y（1）=y″（0）=y″（1）=0where λ is a positive parameter, a ∈ C（[0, 1], （0, ∞）, f ∈C（R,R） satisfies f（u）u 〉 0 for all u ≠ 0. We give conditions on the ratio f（s）/s, at infinity and zero, that guarantee the existence of nodal solutions.The proof of our main results is based upon bifurcation techniques.
基金supported in part by grant from IPM(No.89350020)
文摘The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation on a compact interval[a,b] R{-u＇＇=（λf（x,u）＋g（u））h（u＇）,in（a,b）,u（a）=u（b）=0under ppropriate hypotheses.We exhibit the existence of at least three（weak）solutions and,and the results are illustrated by examples.
