Multiplicity Results for <i>p</i>‐Laplacian with Critical Nonlinearity of Concave‐Convex Type and Sign‐Changing Weight Functions

Tsing‐San Hsu

Type: Article

Publication Date: 2009-01-01

Citations: 26

DOI: https://doi.org/10.1155/2009/652109

Abstract

The multiple results of positive solutions for the following quasilinear elliptic equation: in Ω , u = 0 on ∂ Ω , are established. Here, 0 ∈ Ω is a bounded smooth domain in ℝ N , Δ p denotes the p ‐Laplacian operator, 1 ≤ q < p < N , p ∗ = N p /( N − p ), λ is a positive real parameter, and f , g are continuous functions on which are somewhere positive but which may change sign on Ω . The study is based on the extraction of Palais‐Smale sequences in the Nehari manifold.

Locations

Project Euclid (Cornell University) - View - PDF
DOAJ (DOAJ: Directory of Open Access Journals) - View
Abstract and Applied Analysis - View - PDF

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Works Cited by This (18)

Action	Title	Year	Authors
+	On Neumann boundary value problems for some quasilinear elliptic equations	1997	Paul Binding Pavel Drábek Yin Xi Huang
+	Regularity for a more general class of quasilinear elliptic equations	1984	Peter Tolksdorf
+	On the variational principle	1974	Ivar Ekeland
+	Exact multiplicity for semilinear elliptic Dirichlet problems involving concave and convex nonlinearities	2003	Moxun Tang
+	Boundary regularity for solutions of degenerate elliptic equations	1988	Gary M. Lieberman
+	Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems	1994	Antonio Ambrosetti Haı̈m Brezis G. Cerami
+	On semilinear elliptic equations involving concave–convex nonlinearities and sign-changing weight function	2005	Tsung‐fang Wu
+	On harnack type inequalities and their application to quasilinear elliptic equations	1967	Neil S. Trudinger
+	Minimax Methods in Critical Point Theory with Applications to Differential Equations	1986	P. Rabinowitz
+ PDF Chat	A relation between pointwise convergence of functions and convergence of functionals	1983	Haı̈m Brezis Élliott H. Lieb