EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR DISCRETE $ (P,Q) $-LAPLACIAN PROBLEM WITH NONLINEAR BOUNDARY CONDITIONS

Wujun Pu; Minrui Shi

doi:10.11948/20250370

2026 Volume 16 Issue 5

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Wujun Pu, Minrui Shi. EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR DISCRETE $ (P,Q) $-LAPLACIAN PROBLEM WITH NONLINEAR BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2623-2638. doi: 10.11948/20250370

Citation:

Wujun Pu, Minrui Shi. EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR DISCRETE $ (P,Q) $-LAPLACIAN PROBLEM WITH NONLINEAR BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2623-2638. doi: 10.11948/20250370

EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR DISCRETE $ (P,Q) $-LAPLACIAN PROBLEM WITH NONLINEAR BOUNDARY CONDITIONS

Wujun Pu^1, ,,
Minrui Shi^2,

1.
School of Mathematics and Computer Science, Longnan Normal University, Longnan, Gansu 742500, China
2.
Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730070, China

Author Bio: Email: minrui06120509@163.com(M. Shi)
Corresponding author: Email: Puwj2005@163.com(W. Pu)

Abstract

Abstract

In the present paper, we investigate the existence of positive solutions for a class of singular semi-positive discrete $ (p,q) $-Laplacian problem of second order. Specially, the nonlinear term is singular at $ u=0 $ and may approach $ -\infty $ as $ u\to0^+ $. To overcome the lake of maximum principle, we construct a new comparison theorem. Then, by using Krasnosel'skii type fixed point theorem, we obtain the existence, multiplicity and nonexistence of positive solutions for this kind of problem.
- Discrete (p,q)-Laplacian /
- positive solutions /
- nonlinear boundary conditions /
- Krasnosel'skii-type fixed point theorem /
- existence
MSC: 39A12, 39A27

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References

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