## 6 Citations

### A posteriori verification of the positivity of solutions to elliptic boundary value problems

- Mathematics, Computer SciencePartial Differential Equations and Applications
- 2022

A unified a posteriori method for verifying the positivity of solutions of elliptic boundary value problems by assuming neither H^2 nor L^{\infty} nor H^1_0, and combined with a priori error bounds for Laplacian eigenvalues to obtain a unified method that has wide application.

### A posteriori verification for the sign-change structure of elliptic problems.

- Mathematics
- 2020

This paper proposes a method for rigorously analyzing the sign-change structure of solutions to elliptic problems subject to one of the three types of homogeneous boundary conditions: Dirichlet,…

### A posteriori verification for the sign-change structure of solutions of elliptic partial differential equations

- MathematicsJapan Journal of Industrial and Applied Mathematics
- 2021

This paper proposes a method for rigorously analyzing the sign-change structure of solutions of elliptic partial differential equations subject to one of the three types of homogeneous boundary…

### Rigorous Numerical Enclosures for Positive Solutions of Lane–Emden’s Equation with Sub-Square Exponents

- MathematicsNumerical Functional Analysis and Optimization
- 2022

A method is designed for enclosing the required integrations explicitly, proving the existence of a desired solution based on a generalized Newton-Kantorovich theorem.

### A posteriori verification of the positivity of solutions to elliptic problems

- Mathematics, Computer ScienceArXiv
- 2020

This paper extends one of the approaches and combines it with a priori error bounds for Laplacian eigenvalues to obtain a unified method that has wide application and describes how to evaluate some constants calculated from approximation because the proposed method requires explicit estimates of them.

### Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems

- Mathematics
- 2021

We conﬁrm a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. The method of showing the main chaotic property, a positive…

## References

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### Numerical verification of positiveness for solutions to semilinear elliptic problems

- Mathematics, Computer ScienceJSIAM Lett.
- 2015

A sufficient condition for a solution to an elliptic problem to be positive in the domain of the problem is provided, which can be checked numerically without requiring a complicated computation.

### Numerical verification method for positiveness of solutions to elliptic equations

- Mathematics, Computer Science
- 2016

A sufficient condition for a solution to an elliptic equation to be positive in the domain of the equation is provided, which can be checked numerically without requiring a complicated computation.

### A numerical approach to the proof of existence of solutions for elliptic problems

- Mathematics
- 1988

In this paper, we describe a method which proves by computers the existence of weak solutions for linear elliptic boundary value problems of second order. It is shown that we can constitute the…

### Numerical verification methods for solutions of semilinear elliptic boundary value problems

- Mathematics
- 2011

This article describes a survey on numerical verification methods for second-order semilinear elliptic boundary value problems introduced by authors and their colleagues. Here “numerical…

### A numerical approach to the proof of existence of solutions for elliptic problems II

- Mathematics
- 1988

This paper is a continuation of the preceding study ([2]) in which we described an automatic proof by computer, utilizing Schauder’s fixed point theorem, of the existence of weak solutions for…

### Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation

- Mathematics
- 2014

This paper proposes a verified numerical method of proving the invertibility of linear elliptic operators. This method also provides a verified norm estimation for the inverse operators. This type of…

### On a maximum principle for weak solutions of some quasi-linear elliptic equations

- MathematicsAppl. Math. Lett.
- 2009

### Qualitative properties of positive solutions of semilinear elliptic equations in symmetric domains via the maximum principle

- Mathematics
- 1999

### Sharp numerical inclusion of the best constant for embedding on bounded convex domain

- MathematicsJ. Comput. Appl. Math.
- 2017