where skm are real numbers, pk0(t) ∈ C2[a,b], p00(t)p20(t) = 0, p00(t)/p20(t) > 0 for t ∈ [a,b]. Let s2m < s0m + 2, s2m ≤ s1m + 2, m = 0,1, that is, we consider the case of so-called regular singularities. Operators with irregular singularities possess different qualitative properties and require different investigations. Since the solutions of (1.1) may have singularities at the endpoints of t...

in this paper, we use modified laplace decomposition method to solving initial value problems (ivp) of the second order ordinary differential equations. theproposed method can be applied to linear and nonlinearproblems

Abstract In this paper, we study a singular Finsler double phase problem with nonlinear boundary condition and perturbations that have type of critical growth, even on the boundary. Based variational methods in combination truncation techniques, prove existence at least one weak solution for under very general assumptions. Even case when manifold reduces to Euclidean norm, our work is first dea...

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomials to implement this method. A number of specific numerical examples demonstrate the accuracy and the efficiency of the propos...