Existence of solution for p-Laplacian boundary value problems with two singular and subcritical nonlinearities

Choi, Q-Heung; Jung, Tacksun

doi:10.1186/s13661-019-1210-4

Bound Value Probl

2019

DOI: 10.1186/s13661-019-1210-4

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Existence of solution for p-Laplacian boundary value problems with two singular and subcritical nonlinearities

Q-Heung Choi

Tacksun Jung

Abstract: We consider a boundary value problem for p-Laplacian systems with two singular and subcritical nonlinearities. We obtain one theorem which shows that there exists at least one nontrivial weak solution for these problems under some conditions. We obtain this result by variational method and critical point theory. MSC: 35D30; 35J35; 35J58; 35J75

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2021

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Fractional N-Laplacian Problems Defined on the One-Dimensional Subspace

Choi

Jung

2021

Symmetry

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The research of the fractional Orlicz-Sobolev space and the fractional N-Laplacian operators will give the development of nonlinear elasticity theory, electro rheological fluids, non-Newtonian fluid theory in a porous medium as well as Probability and Analysis as they proved to be accurate models to describe different phenomena in Physics, Finance, Image processing and Ecology. We study the number of weak solutions for one-dimensional fractional N-Laplacian systems in the product of the fractional Orlicz-Sobolev spaces, where the corresponding functionals of one-dimensional fractional N-Laplacian systems are even and symmetric. We obtain two results for these problems. One result is that these problems have at least one nontrivial solution under some conditions. The other result is that these problems also have infinitely many weak solutions on the same conditions. We use the variational approach, critical point theory and homology theory on the product of the fractional Orlicz-Sobolev spaces.

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Fractional N-Laplacian Problems Defined on the One-Dimensional Subspace

Choi

Jung

2021

Symmetry

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show abstract

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Existence of solution for p-Laplacian boundary value problems with two singular and subcritical nonlinearities

Cited by 1 publication

References 18 publications

Fractional N-Laplacian Problems Defined on the One-Dimensional Subspace

Fractional N-Laplacian Problems Defined on the One-Dimensional Subspace

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