On a semilinear fourth order elliptic problem with asymmetric nonlinearity
DOI:
https://doi.org/10.12775/TMNA.2022.028Słowa kluczowe
fourth order operator, a priori estimates, spectral theory, topological degreeAbstrakt
In this work, we address the existence of solutions for a biharmonic elliptic equation with homogeneous Navier boundary condition. The problem is asymmetric and has linear behavior on $-\infty$ and superlinear on $+\infty$. To obtain the results we apply topological methods.Bibliografia
A. Ambrosetti and A. Malchiodi, Nonlinear Analysis and Semilinear Elliptic Problems, Cambridge Studies in Advanced Mathematics, vol. 104, Cambridge University Press, Cambridge, 2007.
E. Berchio, F. Gazzola and E. Mitidieri, Positivity preserving property for a class of biharmonic elliptic problems, J. Differential Equations 229 (2006), 1–23.
H. Brézis and R.E.L. Turner, On a class of superlinear elliptic problems, Comm. Partial Differential Equations 2 (1977), 601–614.
Ph. Clement, D.G. de Figueiredo and E. Mitidieri, A priori estimates for positive solutions of semilinear elliptic systems via Hardy–Sobolev inequalities, Nonlinear Partial Differential Equations (Fés, 1994), Pitman Res. Notes Math. Ser., vol. 343, Longman, Harlow, 1996, pp. 73–91.
F. Cuccu and G. Porru, Optimization of the first eigenvalue in problems involving the bi-Laplacian. Differ. Equ. Appl. 1 (2009), 219–235.
M. Cuesta and C. De Coster, A resonant-superlinear elliptic problem revisited, Adv. Nonlinear Stud. 13 (2013), 97–114.
M. Cuesta and C. De Coster, Superlinear critical resonant problems with small forcing term, Calc. Var. Partial Differential Equations 54 (2015), 349–363.
M. Cuesta, D.G. de Figueiredo and P.N. Srikanth, On a resonant-superlinear elliptic problem, Calc. Var. Partial Differential Equations 17 (2003), 221–233.
D.G. de Figueiredo and J.P. Gossez, Strict monotonicity of eigenvalues and unique continuation, Comm. Partial Differential Equations 17 (1992), 339–346.
F.O. de Paiva and W. Rosa, Neumann problems with resonance in the first eigenvalue, Math. Nachr. 290 (2017), 2198–2206.
F. Gazzola, H.C. Grunau and G. Sweers, Polyharmonic Boundary Value Problems. Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains, Lecture Notes in Mathematics, 1991, Springer–Verlag, Berlin, 2010.
R. Kannan and R. Otega, Superlinear elliptic boundary value problems, Czechoslovak Math. J. 37 (1987), 386–399.
J.R. Ward, Perturbations with some superlinear growth for a class of second order elliptic boundary value problems, Nonlinear Anal. 6 (1982), 367–374.
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Prawa autorskie (c) 2022 Fabiana Ferreira, Everaldo S. Medeiros, Wallisom Rosa
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Bez utworów zależnych 4.0 Międzynarodowe.
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