The Sturm-Liouville theory plays an important role in solving many mathematical physics problems [1].
Namely, we consider the equation of rod bending and the nonlinear Laplace equation that describe many mathematical physics problems like string oscillation, membrane oscillation and so on.
The natural decomposition method (NDM) was first introduced by Rawashdeh and Maitama in 2014 [17 19], to solve linear and nonlinear ODEs and PDEs that appear in many mathematical physics and engineering applications.
The topological fixed point theory is a systematically developed discipline whose powerful methods can be effectively applied in many branches of mathematics, mathematical physics and natural science.
The VIP (1.1) has many applications in computational mathematics, mathematical physics, operations research, mathematical economics, optimization theory, and other fields; see, e.g., [2 5].
VIP (1.2) has many applications in computational mathematics, mathematical physics, operations research, mathematical economics, optimization theory, and other fields; see, e.g., [3 6] and the references therein.
The solution set of VIP (1.1) is denoted by VI ( C, A ). VIP (1.1) was first discussed by Lions [2] and now has many applications in computational mathematics, mathematical physics, operations research, mathematical economics, optimization theory, and other fields; see, e.g., [3 6].
The theory of M-matrix and H-matrix plays an important role in many fields such as computational mathematics, mathematical physics, etc.
When Ω is a smooth bounded domain in R N, the problem { Δ 2 u + c Δ u = f ( x, u ), in Ω, u = Δ u = 0, on ∂ Ω, (1.2). arises in many applications from mathematical physics, which is usually used to describe some phenomena appearing in various physical, engineering, and other sciences.
It is well known that the theory of Sturm-Liouville problems is one of the most actual and extensively developing fields of theoretical and applied mathematics, since it is an important tool in solving many problems in mathematical physics (see [1 4]).
Global analysis has many applications to mathematical physics.
