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

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Springer US
Copyright © 2016 by Springer Science+Business Media New York
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
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