Advances in Differential Equations

A unified approach for multiple constant sign and nodal solutions

D. Motreanu, V. V. Motreanu, and N. S. Papageorgiou

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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.

Article information

Adv. Differential Equations, Volume 12, Number 12 (2007), 1363-1392.

First available in Project Euclid: 18 December 2012

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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.

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