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

By Nikolaos S. Papageorgiou, Vicentiu D. Rădulescu, Dušan D. Repovš. 2016

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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 $$(-\Delta _p,W^{1,p}_{0}(\Omega ))$$(-Δp,W01,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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/690306f69dd02c6b36361c20e77143e771b9b609

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Nonlinear nonhomogeneous singular problems (2019, background): “eorgiou [9], where a similar result is proved for the upper solutions of nonlinear Dirichlet problems without singularities, driven by the p-Laplacian (see also Papageorgiou, Ra˘dulescu & Repovˇs [33, 34], for Robin problems). Proposition 4.1. If hypotheses H(a),H(ϑ),H(f) hold and λ ∈ L = (0,λ∗]”