Abstract
In this article, we prove the existence of a solution to a nonlocal biharmonic equation with nonlinearity depending on the gradient and the Laplacian. We employ an iterative technique based on the mountain pass theorem to prove our result.
Funding source: Science and Engineering Research Board
Award Identifier / Grant number: MTR/2018/000233
Funding statement: Gaurav Dwivedi is supported by Science and Engineering Research Board, India, under the grant no. MTR/2018/000233.
Acknowledgements
The authors thank the referees for a careful review of the manuscript and some useful suggestions.
References
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Estimates for a beam-like partial differential operator and applications
- Stabilization of polynomial systems in ℝ3 via homogeneous feedback
- Analyzing the existence of solution of a fractional order integral equation: A fixed point approach
- Existence of solution to a nonlocal biharmonic problem with dependence on gradient and Laplacian
- Global existence and exponential decay for a viscoelastic equation with not necessarily decreasing kernel
- Solving fractal differential equations via fractal Laplace transforms
- Minimum energy control of degenerate Cauchy problem with skew-Hermitian pencil
- Splines in vibration analysis of non-homogeneous circular plates of quadratic thickness
- The weak eigenfunctions of boundary-value problem with symmetric discontinuities
- Some subclasses of analytic functions involving certain integral operator
- Relation theoretic contractions and their applications in b-metric like spaces
- A new conservative finite difference scheme for 1D Cahn–Hilliard equation coupled with elasticity
- An improved proximal method with quasi-distance for nonconvex multiobjective optimization problem
Artikel in diesem Heft
- Frontmatter
- Estimates for a beam-like partial differential operator and applications
- Stabilization of polynomial systems in ℝ3 via homogeneous feedback
- Analyzing the existence of solution of a fractional order integral equation: A fixed point approach
- Existence of solution to a nonlocal biharmonic problem with dependence on gradient and Laplacian
- Global existence and exponential decay for a viscoelastic equation with not necessarily decreasing kernel
- Solving fractal differential equations via fractal Laplace transforms
- Minimum energy control of degenerate Cauchy problem with skew-Hermitian pencil
- Splines in vibration analysis of non-homogeneous circular plates of quadratic thickness
- The weak eigenfunctions of boundary-value problem with symmetric discontinuities
- Some subclasses of analytic functions involving certain integral operator
- Relation theoretic contractions and their applications in b-metric like spaces
- A new conservative finite difference scheme for 1D Cahn–Hilliard equation coupled with elasticity
- An improved proximal method with quasi-distance for nonconvex multiobjective optimization problem