the investigation of the existence, behavior, and multiplicity of solutions for –p laplacian boundary value problems under the dirichlet boundary conditions

expression and description of most physical and engineering phenomena such as wave propagation, heat transfer, magnetism, etc. lead to the investigation and equational solution of hyperbolic, parabolic, and elliptic kinds. these equations are from basic topics of boundary value and initial value problems. in this paper, we investigate the problem of quasi-linear boundary: −(|𝑢′ |𝑝−2𝑢′ )′ = 𝜆 𝑓(𝑢) 𝑖𝑛 (0,1) 𝑢(0) = 𝑢(1) = 0 where p and ƛ are two actual parameters and p>1, 𝜆 > 0 and f are a nonlinear third-order function. to obtain the number of solutions of the above problem, we use quadrature method.