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An improved interpolating complex variable element-frees Galerkin (IICVEFG) method for the two-dimensional elastic problems is developed. This method is based on the improved interpolating complex variable moving least-squares (IICVMLS) method and the integral form of the elastic problems. In the IICVEFG method, the proposed shape function has the interpolating feature. Therefore, the essential boundary conditions can be exerted directly. Additionally, the unnecessary terms in the discrete matrices are removed, which results in a set of concise formulas. This method is verified by analyzing three elastic examples under different constraints and loads. The numerical results show that the IICVEFG method is superior in precision and efficiency to other non-interpolating meshless methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider generalized Laplacian problems with nonlocal boundary conditions and a singular weight, which may not be integrable. The existence of two positive solutions to the given problem for parameter λ belonging to some open interval is shown. Our approach is based on the fixed point index theory.

A numerical model for the two-dimensional nonlinear elastic–plastic problem is proposed based on the improved interpolating complex variable element free Galerkin (IICVEFG) method and the incremental tangent stiffness matrix method. The viability of the proposed model is verified through three elastic–plastic examples. The numerical analyses show that the IICVEFG method has good convergence. The solutions using the IICVEFG method are consistent with the solutions obtained from the finite element method using the ABAQUS program. Moreover, the IICVEFG method shows greater computing precision and efficiency than the non-interpolating meshless methods.

Abstract Applying a new fixed point theorem due to Radu Precup, this paper investigates the existence and multiplicity of nontrivial radial solutions of coupled system of k -Hessian equations. [ABSTRACT FROM AUTHOR]

In this work, we investigate the existence and multiplicity results for positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions and a parameter $(\mu,\lambda) \in \mathbb{R}_+^3 $. Using sub-super solutions method and fixed point index theorems, it is shown that there exists a continuous surface $\mathcal{C}$ which separates $\mathbb{R}_+^2 \times (0,\infty)$ into two regions $\mathcal{O}_1$ and $\mathcal{O}_2$ such that the problem under consideration has two positive solutions for $( \mu,\lambda) \in \mathcal{O}_1,$ at least one positive solution for $( \mu,\lambda) \in \mathcal{C}$, and no positive solutions for $( \mu,\lambda) \in \mathcal{O}_2.$

In this work, we investigate the existence and multiplicity results for positive solutions to a singular (p1, p2)-Laplacian system with coupled integral boundary conditions and a parameter (μ, λ) ∊ R3+. Using sub-super solutions method and fixed point index theorems, it is shown that there exists a continuous surface C which separates R2+ x(0,∞) into two regions O1 and O2 such that the problem under consideration has two positive solutions for (μ, λ)∊ O1, at least one positive solution for ((μ, λ)∊ C, and no positive solutions for ((μ, λ)∊ O2. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to consider a class of k i -Hessian systems with singular weight functions. Among others, we obtain new results on the existence and multiplicity of positive solutions. Moreover, many positive solutions are also considered. [ABSTRACT FROM AUTHOR]

We study the weighted heat trace asymptotics of an operator of Laplace type with mixed boundary conditions where the weight function exhibits radial blowup. We give formulas for the first three boundary terms in the expansion in terms of geometrical data. [ABSTRACT FROM AUTHOR]

In this paper, we consider generalized Laplacian problems with nonlocal boundary conditions and a singular weight, which may not be integrable. The existence of two positive solutions to the given problem for parameter λ belonging to some open interval is shown. Our approach is based on the fixed point index theory. [ABSTRACT FROM AUTHOR]

A numerical model for the two-dimensional nonlinear elastic–plastic problem is proposed based on the improved interpolating complex variable element free Galerkin (IICVEFG) method and the incremental tangent stiffness matrix method. The viability of the proposed model is verified through three elastic–plastic examples. The numerical analyses show that the IICVEFG method has good convergence. The solutions using the IICVEFG method are consistent with the solutions obtained from the finite element method using the ABAQUS program. Moreover, the IICVEFG method shows greater computing precision and efficiency than the non-interpolating meshless methods. [ABSTRACT FROM AUTHOR]