Existence and Properties of the Solutions via Fibering Method  of a Class of Variational Equations with Non-Coercive Main Part  with Some Applications

Luisa Toscano

doi:10.15866/irease.v12i6.18584

Existence and Properties of the Solutions via Fibering Method of a Class of Variational Equations with Non-Coercive Main Part with Some Applications

Luisa Toscano^(1*)

^(*) Corresponding author

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DOI: https://doi.org/10.15866/irease.v12i6.18584

Abstract

Many physical problems, such as in fluidodynamics or aerospace applications, are governed by systems of differential equations with nonlinearity of nonlocal type, too. Obviously, the main question is the existence of the solutions of such problems but it is also interesting to analyze the properties of these solutions, when it is possible. In order to find the existence of the solutions and the related properties, this paper proposes to adopt a theorem previously proved by the same author. Following a variational approach via fibering method in the paper a class of variational equations with non-coercive main part has been used to solve differential equations of some interesting applications.
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Keywords

Variational Equations; Fibering Idea; Lagrange Multipliers

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References

Toscano, L., Second Existence Theorem for a Class of Variational Equations with Non-Coercive Main Part, (2019) International Review on Modelling and Simulations (IREMOS), 12 (5), pp. 335-340.
https://doi.org/10.15866/iremos.v12i5.18515

Toscano, L., Existence Theorems for a General Variational Equation with Non Coercive Main Part, (2017) International Review on Modelling and Simulations (IREMOS), 10 (6), pp. 378-391.
https://doi.org/10.15866/iremos.v10i6.13289

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.
https://doi.org/10.1080/09720502.2011.10700741

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.
https://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.
https://doi.org/10.15866/iremos.v8i5.7869

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).
https://doi.org/10.1155/2016/1683759

S.I. Pohozaev, Periodic solutions of certain nonlinear systems of ordinary differential equations, Diff. Uravn., 1980, vol 16, n.1, pp.109-116.

S.I. Pohozaev, On the global fibering method in nonlinear variational problems, Proc. Steklov Inst. of Math. 219 (1997), 281-328.

S.I. Pohozaev, L. Véron, Multiple positive solutions of some quasilinear Neumann problems, Applicable Analysis 74 (2000), 363-390.
https://doi.org/10.1080/00036810008840822

A.M. Piccirillo, L. Toscano, S. Toscano, On the solvability of some nonlinear Neumann problems, Advanced Nonlinear Studies 1, n.1 (2001), 102-119.
https://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.
https://doi.org/10.1515/ans-2001-0204

Y.Bozhkov, E.Mitidieri, Existence of multiple solutions for quasilinear systems via fibering method, J.Diff.Eq. 190 (2003), 239-267.
https://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, Birkhäuser Verlag Basel (2003).
https://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,Control and Optimization 26 (2006) 113-121.
https://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.
https://doi.org/10.1016/j.phpro.2012.05.321

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