Positive Lp-solutions of subcritical nonlinear problems

Nonexistence of Positive Solutions of Nonlinear Boundary Value Problems

We discuss the nonexistence of positive solutions for nonlinear boundary value problems. In particular, we discuss necessary restrictions on parameters in nonlocal problems in order that (strictly) positive solutions exist. We consider cases that can be written in an equivalent integral equation form which covers a wide range of problems. In contrast to previous work, we do not use concavity ar...

Existence of Three Positive Solutions to Nonlinear Boundary Value Problems

Multiple Positive Solutions of Nonlinear Boundary Value Problems

where w, p are positive and continuous on (0, 1), which allows singularities at the endpoints, and f(y) ≥ 0 and continuous for y ∈ R. For a given positive integer N , we provide conditions on the nonlinear function f which guarantee existence of N positive solutions. Our motivation comes from previous work in the case w(x) ≡ p(x) ≡ 1 of Henderson and Thompson [6], which uses a fixed point theor...

Positive Solutions of Second Order Nonlinear Difference Boundary Value Problems

We study a class of second order nonlinear difference boundary value problems with separated boundary conditions. A series of criteria are obtained for the existence of one, two, arbitrary number, and even an infinite number of positive solutions. A theorem for the nonexistence of positive solutions is also derived. Several examples are given to demonstrate the applications. Our results improve...

Positive solutions of nonlinear second-order periodic boundary value problems

Ruyun Ma, Chenghua Gao, and Ruipeng Chen Department of Mathematics, Northwest Normal University, Lanzhou 730070, China Correspondence should be addressed to Ruyun Ma, ruyun [email protected] Received 31 August 2010; Revised 30 October 2010; Accepted 8 November 2010 Academic Editor: Irena Rachůnková Copyright q 2010 Ruyun Ma et al. This is an open access article distributed under the Creative Commons A...