# On a Class of Parametric (p,2)-equations

On a Class of Parametric (p,2)-equations We consider parametric equations driven by the sum of a p-Laplacian and a Laplace operator (the so-called (p, 2)-equations). We study the existence and multiplicity of solutions when the parameter $$\lambda >0$$ λ > 0 is near the principal eigenvalue $$\hat{\lambda }_1(p)>0$$ λ ^ 1 ( p ) > 0 of $$(-\Delta _p,W^{1,p}_{0}(\Omega ))$$ ( - Δ p , W 0 1 , p ( Ω ) ) . We prove multiplicity results with precise sign information when the near resonance occurs from above and from below of $$\hat{\lambda }_1(p)>0$$ λ ^ 1 ( p ) > 0 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# On a Class of Parametric (p,2)-equations

, Volume 75 (2) – Jan 22, 2016
36 pages

/lp/springer_journal/on-a-class-of-parametric-p-2-equations-7l6VWr3g0v
Publisher
Springer US
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-016-9330-z
Publisher site
See Article on Publisher Site

### Abstract

We consider parametric equations driven by the sum of a p-Laplacian and a Laplace operator (the so-called (p, 2)-equations). We study the existence and multiplicity of solutions when the parameter $$\lambda >0$$ λ > 0 is near the principal eigenvalue $$\hat{\lambda }_1(p)>0$$ λ ^ 1 ( p ) > 0 of $$(-\Delta _p,W^{1,p}_{0}(\Omega ))$$ ( - Δ p , W 0 1 , p ( Ω ) ) . We prove multiplicity results with precise sign information when the near resonance occurs from above and from below of $$\hat{\lambda }_1(p)>0$$ λ ^ 1 ( p ) > 0 .

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jan 22, 2016

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