Existence of multiple and sign-changing solutions for a problem involving p-Laplacian and jumping nonlinearities are considered via the construction of descent flow in C 1 0 ð % OÞ: Signchanging and multiple solutions are obtained under additional assumption on the nonlinearity. The uniqueness of positive (negative) solution theorem is included too. r
This paper contains three parts. In the first part, we determine the best constant of an improved inequality of Gagliardo-Nirenberg interpolation (Chen, in Czechoslov Math J, in press). In the second part, we use this best constant to establish a sharp criterion for the global existence and blow-up of solutions of the inhomogeneous nonlinear Schrödinger equation with harmonic potentialin the critical nonlinearity p = 1 + (4 + 2b)/N . In the third part, we use this best constant to construct an unbounded subset S of and prove that the solutions exist globally in time for ϕ 0 ∈ S and p > 1 + (4 + 2b)/N .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.