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EXISTENCE OF THREE SOLUTIONS FOR EQUATIONS OF p(x)-LAPLACE TYPE

이승대|김연호
장전수학회 (Jangjeon Mathematical Society)|2017.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제20권 제2호|pp. 245-260|DOI 10.17777/pjms.2017.20.2.011

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참고문헌

키워드

p(x)-Laplace type operatorVariable exponent Lebesgue-Sobolev spacesWeak solutionsThree-critical-points theorem
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초록

We are concerned with the following elliptic equations with variable exponents 􀀀div('(x;ru)) = f(x; u) + g(x; u) in ; which is subject to Dirichlet boundary condition. The purpose of this paper is to establish the existence of at least three solutions for the problem above by using as the main tool a variational principle due to Ricceri. In addition, we give information on size and location of an interval of 's for which the given problem has either only the trivial solution or at least two nontrivial solutions.

Abstract

We are concerned with the following elliptic equations with variable exponents 􀀀div('(x;ru)) = f(x; u) + g(x; u) in ; which is subject to Dirichlet boundary condition. The purpose of this paper is to establish the existence of at least three solutions for the problem above by using as the main tool a variational principle due to Ricceri. In addition, we give information on size and location of an interval of 's for which the given problem has either only the trivial solution or at least two nontrivial solutions.

참고문헌 (24)

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