Title: Forced oscillation of nonlinear elliptic partial differential equations

Authors: Balamani Shanmugam; George E. Chatzarakis; Sadhasivam Vadivel; Priyadharshini Sundaravadivel

Addresses: Post-Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College, Rasipuram – 637401, Namakkal Dt., Tamil Nadu, India ' Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education (ASPETE), Marousi, 15122, Athens, Greece ' Post-Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College, Rasipuram – 637401, Namakkal Dt., Tamil Nadu, India ' Post-Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College, Rasipuram – 637401, Namakkal Dt., Tamil Nadu, India

Abstract: The main objective of this paper is to investigate the oscillatory behaviour of the solutions of the nonlinear elliptic partial differential equations by using the Riccati technique and the integral average method. Our main goal is to establish (1.1) reduced to an ordinary differential equation by using r = | x |. Radial solutions r often arise in the problems with rotational or spherical symmetry and their study is crucial in various fields such as physics, engineering and biology. If D(r) = 0, equation (1.1) becomes a superlinear elliptic equation. If C(r) = 0, equation (1.1) becomes a sublinear elliptic equation. If either λ = 1, D(r) = 0 or C(r) = 0, μ = 1, then (1.1) is reduced to linear elliptic partial differential equations. We have provided examples to show the effectiveness of our results.

Keywords: oscillation; nonlinear; elliptic partial differential equations.

DOI: 10.1504/IJDSDE.2026.154418

International Journal of Dynamical Systems and Differential Equations, 2026 Vol.15 No.1, pp.71 - 81

Received: 18 Sep 2024
Accepted: 23 Jun 2025
Published online: 26 Jun 2026 *

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