Mathematics > Home > Advances in Pure and Applied Mathematics > Issue 4 (September 2021) > Article
NAWAL IRZI
University of Tunis El Manar
Tunisia
Published on 6 September 2021 DOI : 10.21494/ISTE.OP.2021.0722
This paper is devoted to the study of the nonhomogeneous problem
where is a bounded smooth domain in are positive real numbers, is a potential, is a continuous function, is mapping such that is increasing homeomorphism from ℝ to ℝ and is a continuous function. We establish there main results with various assumptions, the first one asserts that any 0> is an eigenvalue of our problem. The second Theorem states the existence of a constant such that every is an eigenvalue of the problem. While the third Theorem claims the existence of a constant such that every is an eigenvalue of the problem. Our approach relies on adequate variational methods in Orlicz-Sobolev spaces.
This paper is devoted to the study of the nonhomogeneous problem
where is a bounded smooth domain in are positive real numbers, is a potential, is a continuous function, is mapping such that is increasing homeomorphism from ℝ to ℝ and is a continuous function. We establish there main results with various assumptions, the first one asserts that any 0> is an eigenvalue of our problem. The second Theorem states the existence of a constant such that every is an eigenvalue of the problem. While the third Theorem claims the existence of a constant such that every is an eigenvalue of the problem. Our approach relies on adequate variational methods in Orlicz-Sobolev spaces.
Mountain pass Theorem Ekeland’s variational principle Orlicz-Sobolev space.
Ekeland’s variational principle Mountain pass Theorem Orlicz-Sobolev space.