EXISTENCE RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM DRIVEN BY A NON-HOMOGENEOUS OPERATOR

John R. Graef; Shapour Heidarkhani; Lingju Kong; Shahin Moradi

doi:10.11948/20240147

2025 Volume 15 Issue 1

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John R. Graef, Shapour Heidarkhani, Lingju Kong, Shahin Moradi. EXISTENCE RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM DRIVEN BY A NON-HOMOGENEOUS OPERATOR[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 547-563. doi: 10.11948/20240147

Citation:

John R. Graef, Shapour Heidarkhani, Lingju Kong, Shahin Moradi. EXISTENCE RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM DRIVEN BY A NON-HOMOGENEOUS OPERATOR[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 547-563. doi: 10.11948/20240147

EXISTENCE RESULTS FOR A NONLINEAR ELLIPTIC PROBLEM DRIVEN BY A NON-HOMOGENEOUS OPERATOR

1.
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
2.
Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah 67149, Iran

Author Bio: Email: s.heidarkhani@razi.ac.ir(S. Heidarkhani); Email: Lingju-Kong@utc.edu(L. Kong); Email: shahin.moradi86@yahoo.com(S. Moradi)
Corresponding author: Email: John-Graef@utc.edu(J. R. Graef)

Abstract

Abstract

In this paper, the authors discuss the existence of at least one weak solution and infinitely many weak solutions to a parametric nonlinear Dirichlet problem involving a nonhomogeneous differential operator of $ p $-Laplacian type. Their approach is based on variational methods. Some recent results are extended and improved, and an example is presented to demonstrate the application of the main results.
- Nonlinear elliptic problem /
- one weak solution /
- infinitely many solutions /
- variational methods
MSC: 34B15, 35J15

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References

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