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Existence Theorems for a General Variational Equation with Non Coercive Main Part
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DOI: https://doi.org/10.15866/iremos.v10i6.13289
Abstract
By using the fibering method, we study the solvability of a general variational equation with non coercive main part in a real and reflexive Banach space. The results we get in this paper are useful for searching weak solutions of many problems connected to nonlinear differential homogeneous equations.
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References
L. Toscano, S. Toscano, On the solvability of a class of general systems of variational equations with nonmonotone operators, Journal of Interdisciplinary Mathematics 14, n.2, (2011), 123-147.
http://dx.doi.org/10.1080/09720502.2011.10700741
L. Toscano, S. Toscano, A new result concerning the solvability of a class of general systems of variational equations with nonmonotone operators:applications to Dirichlet and Neumann nonlinear problems, Intenational Journal of Differential Equations vol.2016 (2016).
http://dx.doi.org/10.1155/2016/1683759
S.I. Pohozaev, On the global fibering method in nonlinear variational problems, Proc. Steklov Inst. of Math. 219 (1997), 281-328.
P. Drabek, S. I. Pohozaev, Positive solutions for the p-Laplacian: application of the fibering method, Proc. of Roy. Soc. Edinburgh 127A, n.3 (1997), 703-726.
S.I. Pohozaev, A. Tesei, Existence of positive solutions to some nonlinear Neumann problems, Dokl. Acad. Nauk 363, n.4 (1998), 450-453.
S.I. Pohozaev, L. Véron, Multiple positive solutions of some quasilinear Neumann problems, Applicable Analysis 74 (2000), 363-390.
http://dx.doi.org/10.1080/00036810008840822
A.M. Piccirillo, R. Toscano, Multiple solutions of some nonlinear elliptic problems containing the p-Laplacian, Differential Equations, 37, n.8 (2001), 1121-1132.
http://dx.doi.org/10.1023/a:1012471502824
A.M. Piccirillo, L. Toscano, S. Toscano, On the solvability of some nonlinear Neumann problems, Advanced Nonlinear Studies 1, n.1 (2001), 102-119.
http://dx.doi.org/10.1515/ans-2001-0106
A.M. Piccirillo, L. Toscano, S. Toscano, On the solvability of some nonlinear systems of elliptic equations, Advanced Nonlinear Studies 1, n.2 (2001), 89-115.
http://dx.doi.org/10.1515/ans-2001-0204
Y.Bozhkov, E.Mitidieri, Existence of multiple solutions for quasilinear systems via fibering method, JDE 190 (2001), 239-267.
http://dx.doi.org/10.1016/s0022-0396(02)00112-2
Y.Il’yasov, T.Runst, Nonlocal Investigations of Inhomogeneous Indefinite Elliptic Equations via Variational Methods, Function Spaces, Differential Operators and Nonlinear Analysis. The Hans Triebel Anniversary Volume, Birkäuser Verlag Basel (2003).
http://dx.doi.org/10.1007/978-3-0348-8035-0_23
D.A.Kandilakis, M.Magiropoulos, A Fibering Method Approach to a System of Quasilinear Equations with Nonlinear Boundary Conditions, Discussiones Mathematicae, Differential Inclusions, Contol and Optimization 26 (2006) 113-121.
http://dx.doi.org/10.7151/dmdico.1068
B.Xu,P.Yanfang, Existence of Solutions for P-laplace Equation with Critical Exponent, Physics Procedia 33 (2012) 2040-2044.
http://dx.doi.org/10.1016/j.phpro.2012.05.321
L. Toscano, S. Toscano, Dirichlet and Neumann problems related to nonlinear elliptic systems: solvability, multiple solutions, solutions with positive components, Abstract and Applied Analysis (2012), 1-44.
http://dx.doi.org/10.1155/2012/760854
Toscano, L., Toscano, S., A New Approach for the Existence of Time Periodic Solutions of Special Classes of Nonlinear Problems, (2015) International Review on Modelling and Simulations (IREMOS), 8 (5), pp. 512-532.
http://dx.doi.org/10.15866/iremos.v8i5.7869
P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations 51 (1984), 126-50.
http://dx.doi.org/10.1016/0022-0396(84)90105-0
N.S. Trudinger, On Harnack type inequalities and their application to quasilinear elliptic equations, Comm. Pure. Appl. Math. 20 (1967), 721-747.
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