there exist solutions

USAGE SUMMARY

The phrase "there exist solutions" is correct and usable in written English.
It can be used in mathematical or scientific contexts to indicate that solutions to a problem or equation are available or can be found. Example: "In this equation, there exist solutions that satisfy the given conditions."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

38 human-written examples

It is shown that for small parameters there exist solutions which concentrate on manifolds of dimensions one, three and seven, which are given as Hopf-fibres.

Journal of Functional Analysis

Also analytic and continuous extensions of solutions to homogeneous Dirac equations are studied, and it is shown that for each cell of harmonicity considered here there exist solutions to each iterate of the Dirac operator which may not be extended beyond any point of the closure of the cell.

Journal of Functional Analysis

In fact, there exist solutions such that for, has exactly simple zeros on the open interval and and there exist solutions such that for, has exactly simple zeros on the open interval and.

Boundary Value Problems

Assume that (1/τ, 1/θ) < (0, 0), then there exist solutions of (1.1) being globally bounded.

Boundary Value Problems

Thus it has been concluded that under some assumptions on the function K, there exist solutions of the nonlinear problem ((S_{varepsilon})) which are concentrated at two different points of the boundary.

Journal of Inequalities and Applications

In view of (6), one can easily see that (L_{n}(r)) has a local minimum in the interior of (S_{delta }), thus there exist solutions to equation (4).

Advances in Difference Equations

Human-verified similar examples from authoritative sources

Similar Expressions

22 human-written examples

Then there exists solution to evolutionary quasivariational inequality (3.41).

Journal of Inequalities and Applications

Since the optimization problem belongs to an under-determined system, there exist multiple solutions.

BMC Systems Biology

For several cases there exist analytical solutions for this ODE system, which have been reported elsewhere [ 3, 5].

BMC Systems Biology

if Eq. (1.8) has a solution, then there exists a solution of the inverse problem (1.1)–(1.1).

Bulletin of Mathematical Sciences

That is there exists a solution of the problem: where.

Fixed Point Theory and Applications

Expert writing Tips

Best practice

In scientific writing, use "there exist solutions" to formally assert the presence of solutions to a specific problem or equation. Ensure that the context clearly defines the problem and the criteria for a valid solution.

Common error

Avoid using "there exist solutions" in informal writing. Opt for simpler alternatives like "solutions are available" or "we can find solutions" to maintain a natural and accessible tone.

Linguistic Context

The phrase "there exist solutions" functions as an existential quantifier, asserting the presence of at least one solution within a specified context. Ludwig AI confirms its correctness and usability, particularly in mathematical and scientific discussions.

Expression frequency: Uncommon

Frequent in

Science

90%

Academia

5%

News & Media

2%

Less common in

Formal & Business

1%

Wiki

1%

Reference

1%

Ludwig's WRAP-UP

In summary, "there exist solutions" is a grammatically correct and formal phrase primarily used in scientific and mathematical contexts to assert the presence of at least one solution to a specific problem or equation. According to Ludwig AI, while accurate, it is advisable to consider simpler alternatives in less formal contexts. The phrase is mostly found in scientific literature, emphasizing its suitability for academic and research-oriented writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

solutions are present

Focuses on the presence of solutions, simplifying the wording.

solutions are available

Indicates solutions are accessible or obtainable.

solutions can be found

Emphasizes the possibility of discovering solutions.

solutions are demonstrable

Highlights that solutions can be proven or shown.

solutions are provable

Focuses on the mathematical or logical provability of solutions.

solutions are achievable

Emphasizes that solutions can be reached or attained.

solutions materialize

Describes solutions coming into existence, often unexpectedly.

solutions emerge

Similar to materialize, but implies a gradual appearance of solutions.

the existence of solutions is confirmed

Formally asserts that solutions are validated or verified.

the existence of solutions is established

Indicates that the solutions have been proven or demonstrated.

FAQs

How do I use "there exist solutions" in a sentence?

Use "there exist solutions" to formally state that solutions to a problem or equation are present. For example: "For this differential equation, there exist solutions that satisfy the initial conditions."

What can I say instead of "there exist solutions"?

You can use alternatives like "solutions are available", "solutions can be found", or "solutions are present" depending on the context.

Is it more appropriate to use "there exist solutions" or "solutions exist"?

"There exist solutions" is more formal and emphatic, often used in mathematical or scientific contexts. "Solutions exist" is a simpler, more direct statement. The choice depends on the desired level of formality and emphasis.

What does it mean when we say "there exist solutions" in mathematics?

In mathematics, "there exist solutions" means that at least one solution to a given equation or problem can be proven to exist, even if the specific solution is not explicitly known.