Geodesic
Asymmetric, Noncoercive, Superlinear (p,2)-Equations
Journal of convex analysis, Tome 24 (2017) no. 3, pp. 769-793
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We examine a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a $p$-Laplacian $(p\geq 2)$ and a Laplacian (a $(p,2)$-equation). The reaction term is asymmetric and it is superlinear in the positive direction and sublinear in the negative direction. The superlinearity is not expressed using the Ambrosetti-Rabinowitz condition, while the asymptotic behavior as $x\rightarrow-\infty$ permits resonance with respect to any nonprincipal eigenvalue of $(-\Delta_p,W^{1,p}_{0}(\Omega))$. Using variational methods based on the critical point theory and Morse theory (critical groups), we prove a multiplicity theorem producing three nontrivial solutions.
Classification : 35J20, 35J60, 58E05
Mots-clés : (p,2)-equation, asymmetric reaction, superlinear growth, multiple solutions, nonlinear regularity, critical groups 
@article{JCA_2017_24_3_JCA_2017_24_3_a2,
     author = {N. S. Papageorgiou and V. D. Radulescu},
     title = {Asymmetric, {Noncoercive,} {Superlinear} {(p,2)-Equations}},
     journal = {Journal of convex analysis},
     pages = {769--793},
     year = {2017},
     volume = {24},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_3_JCA_2017_24_3_a2/}
}
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N. S. Papageorgiou; V. D. Radulescu. Asymmetric, Noncoercive, Superlinear (p,2)-Equations. Journal of convex analysis, Tome 24 (2017) no. 3, pp. 769-793. http://geodesic.mathdoc.fr/item/JCA_2017_24_3_JCA_2017_24_3_a2/