Existence Theorems for a General Variational Equation with Non Coercive Main Part

Luisa Toscano(1*)

(1) Dept. of Math. and Appl. ”R. Caccioppoli”, Univ. of Naples “Federico II”, via Cintia, Monte S. Angelo, Italy
(*) Corresponding author



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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Keywords


Noncoercive Lagrangian Multipliers Fibering

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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.

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).

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.

A.M. Piccirillo, R. Toscano, Multiple solutions of some nonlinear elliptic problems containing the p-Laplacian, Differential Equations, 37, n.8 (2001), 1121-1132.

A.M. Piccirillo, L. Toscano, S. Toscano, On the solvability of some nonlinear Neumann problems, Advanced Nonlinear Studies 1, n.1 (2001), 102-119.

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.

Y.Bozhkov, E.Mitidieri, Existence of multiple solutions for quasilinear systems via fibering method, JDE 190 (2001), 239-267.

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).

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.

B.Xu,P.Yanfang, Existence of Solutions for P-laplace Equation with Critical Exponent, Physics Procedia 33 (2012) 2040-2044.

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.

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.

P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations 51 (1984), 126-50.

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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