Advances in Differential Equations
- Adv. Differential Equations
- Volume 12, Number 12 (2007), 1363-1392.
A unified approach for multiple constant sign and nodal solutions
We consider a nonlinear elliptic equation driven by the $p$-Laplacian with Dirichlet boundary condition. Using variational techniques, combined with the method of upper-lower solutions and suitable truncation arguments, we establish the existence of at least six nontrivial solutions: two positive, two negative and two nodal (sign-changing) solutions. Our framework of analysis incorporates both coercive and $p-1$-superlinear problems. Also, the result on multiple constant sign solution incorporates the case of concave-convex nonlinearities.
Adv. Differential Equations, Volume 12, Number 12 (2007), 1363-1392.
First available in Project Euclid: 18 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35J20: Variational methods for second-order elliptic equations 35J25: Boundary value problems for second-order elliptic equations 47J30: Variational methods [See also 58Exx] 49R50
Motreanu, D.; Motreanu, V. V.; Papageorgiou, N. S. A unified approach for multiple constant sign and nodal solutions. Adv. Differential Equations 12 (2007), no. 12, 1363--1392. https://projecteuclid.org/euclid.ade/1355867406