Local minimizers over the Nehari manifold for a class of concave-convex problems with sign changing nonlinearity

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Multiplicity Results for p-Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight Functions

and Applied Analysis 3 Theorem 1.3 see 5 . There exists λ0 > 0 such that 1.4 admits exactly two solutions for λ ∈ 0, λ0 , exactly one solution for λ λ0, and no solution for λ > λ0. To proceed, wemake somemotivations of the present paper. Recently, in 6 the author has considered 1.2 with subcritical nonlinearity of concave-convex type, g ≡ 1, and f is a continuous function which changes sign in ...

Multiple Positive Solutions for a Class of Concave-Convex Semilinear Elliptic Equations in Unbounded Domains with Sign-Changing Weights

Correspondence should be addressed to Tsing-San Hsu, [email protected] Received 8 September 2010; Accepted 18 October 2010 Academic Editor: Julio Rossi Copyright q 2010 Tsing-San Hsu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly c...

the nehari manifold for a class of indefinite weight semilinear elliptic equations

Exact Multiplicity of Solutions for Classes of Semipositone Problems with Concave-convex Nonlinearity

where λ is a positive parameter. The nonlinearity f(u) is called semipositone if f(0) < 0. In this paper we will only consider the positive solutions of (1.1). Semipositone problems were introduced by Castro and Shivaji in [CS1], and they arise from various disciplines, like astrophysics and population dynamics. (see [CMS] for more details.) It is possible that (1.1) has non-negative solutions ...