This paper investigates the boundary value problem for elastic beam equation of the formu″″（t） q（t）f（t, u（t）,u′（t）,u″（t）,u′″（t））, 0〈t〈1,with the boundary conditionsu=（0）=u′（1）=u″（0）=u′″...This paper investigates the boundary value problem for elastic beam equation of the formu″″（t） q（t）f（t, u（t）,u′（t）,u″（t）,u′″（t））, 0〈t〈1,with the boundary conditionsu=（0）=u′（1）=u″（0）=u′″（1）=0.The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. By using Leray-Schauder nonlinear alternate, Leray-Schauder fixed point theorem and a fixed point theorem due to Avery and Peterson, we establish some results on the existence and multiplicity of positive solutions to the boundary value problem. Our results extend and improve some recent work in the literature.展开更多
We investigate a fractional p-Laplacian equation with right-hand-side nonlinearity which exhibits (p-1)-sublinear term of the formλ|u|q-2,q < p (concave term),and a continuous term f(x,u) which is respectively (p-...We investigate a fractional p-Laplacian equation with right-hand-side nonlinearity which exhibits (p-1)-sublinear term of the formλ|u|q-2,q < p (concave term),and a continuous term f(x,u) which is respectively (p-1)-superlinear or asymptotically (p-1)-linear at infinity.Some existence results for multiple nontrivial solutions are established by using variational methods combined with the Morse theory.展开更多
基金supported by the Natural Science Foundation of Zhejiang Province of China (Y605144)
文摘This paper investigates the boundary value problem for elastic beam equation of the formu″″（t） q（t）f（t, u（t）,u′（t）,u″（t）,u′″（t））, 0〈t〈1,with the boundary conditionsu=（0）=u′（1）=u″（0）=u′″（1）=0.The boundary conditions describe the deformation of an elastic beam simply supported at left and clamped at right by sliding clamps. By using Leray-Schauder nonlinear alternate, Leray-Schauder fixed point theorem and a fixed point theorem due to Avery and Peterson, we establish some results on the existence and multiplicity of positive solutions to the boundary value problem. Our results extend and improve some recent work in the literature.
基金This research is supported by the NSFC(Nos.11661070,11764035 and 11571176).
文摘We investigate a fractional p-Laplacian equation with right-hand-side nonlinearity which exhibits (p-1)-sublinear term of the formλ|u|q-2,q < p (concave term),and a continuous term f(x,u) which is respectively (p-1)-superlinear or asymptotically (p-1)-linear at infinity.Some existence results for multiple nontrivial solutions are established by using variational methods combined with the Morse theory.
