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The Existence of Nontrivial Solutions for Two Class of Strongly Indefinite Elliptic Systems

Author: SunYi
Tutor: ShiShaoYun
School: Jilin University
Course: Basic mathematics
Keywords: Strongly Indefinite Elliptic System ε Critical Group Gen-eralized Linking Theorem Monotonicity Technique
CLC: O175.25
Type: PhD thesis
Year: 2013
Downloads: 22
Quote: 0
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Abstract


The strongly indefinite elliptic system is related to the reaction-difusionsystems appeared in chemical and biological phenomena. In this paper wewill consider the existence of nontrivial solutions for two class of stronglyindefinite elliptic systems by using variational methods.In the second chapter we consider a class of noncooperative ellipticsystemswhereΩ R2Nis a bounded and smooth domain. Assume that the sys-tem is asymptotically linear and resonant at infinity. By using the infinitedimensional Morse theory established by Kryszewski, Szulkin and penal-ized functional technique, we obtain the existence of nontrivial solutionsfor this elliptic system.In the third chapter we consider a class of Hamiltonian elliptic systemdefined on the whole space where N≥3, V (x)∈C(RN, R), the nonlinearity f, g∈C(RN×R, R) areperiodic with respect to x and superlinear at infinity. By using the gen-eralized linking theorem established by Kryszewski, Szulkin and a mono-tonicity trick, we obtain the existence of nontrivial ground state for thesystem.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Elliptic equations
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