EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR PERTURBED KIRCHHOFF TYPE ELLIPTIC PROBLEMS WITH HARDY POTENTIAL

• Published in: TWMS journal of applied and engineering mathematics Vol. 9; no. 3; p. 500
• Main Authors: Roudbari, S.P, Afrouzi, G.A
• Format: Journal Article
• Language: English
• Published: Istanbul Turkic World Mathematical Society 01.01.2019; Elman Hasanoglu
• Subjects: Biharmonic equations; Boundary conditions; Boundary value problems; Coercivity; Critical point; Eigenvalues; Existence theorems; Mathematical analysis; Mathematical research; Nonlinearity; Partial differential equations; Variational methods; Iran
• ISSN: 2146-1147; 2146-1147

In this paper, we prove the existence of at least three weak solutions for a doubly eigenvalue elliptic systems involving the p-biharmonic equation with Hardy potential of Kirchhoff type with Navier boundary condition. More precisely, by using variational methods and three critical points theorem due to B. Ricceri, we establish multiplicity results on the existence of weak solutions for such problems where the reaction term is a nonlinearity function f which satisfies in the some convenient growth conditions. Indeed, using a consequence of the critical point theorem due to Ricceri, which in it the coercivity of the energy Euler functional was required and is important, we attempt the existence of multiplicity solutions for our problem under algebraic conditions on the nonlinear parts. We also give an explicit example to illustrate the obtained result. Keywords: Multiplicity of weak solutions, perturbed Kirchhoff type elliptic problems, Hardy potential, Critical points. AMS Subject Classification: 35J35, 35J60