Multiplicity of solutions for quasilinear elliptic equations

Large Solutions for Quasilinear Elliptic Equations

Multiplicity of solutions for quasilinear elliptic boundary-value problems

This paper is concerned with the existence of multiple solutions to the boundary-value problem −(φp(u )) = λφq(u) + f(u) in (0, 1) , u(0) = u(1) = 0 , where p, q > 1, φx(y) = |y| y, λ is a real parameter, and f is a function which may be sublinear, superlinear, or asymmetric. We use the time map method for showing the existence of solutions.

Positive Solutions of Quasilinear Elliptic Equations

(1.2) { −∆pu = λa(x)|u|p−2u, u ∈ D 0 (Ω), has the least eigenvalue λ1 > 0 with a positive eigenfunction e1 and λ1 is the only eigenvalue having this property (cf. Proposition 3.1). This gives us a possibility to study the existence of an unbounded branch of positive solutions bifurcating from (λ1, 0). When Ω is bounded, the result is well-known, we refer to the survey article of Amann [2] and t...

Multiplicity of solutions to elliptic equations

The case of singular potentials in second order problems and Morse theory in a fourth order problem To my family, and in particular to Marco. To our friends, who always help us in growing up.

Existence and Multiplicity of Positive Solutions to a Class of Quasilinear Elliptic Equations in RN

Correspondence should be addressed to Tsing-San Hsu, [email protected] Received 9 October 2009; Accepted 12 February 2010 Academic Editor: Kanishka Perera 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 properl...