Такая проблема существует.

Такая means such or this kind of here.

So Такая проблема существует is literally something like:

• Such a problem exists
• This kind of problem exists

It usually points to a type of problem that has just been mentioned or is understood from context.

Because такая has to agree with проблема.

Проблема is:

• feminine
• singular
• nominative

So the matching form of такой is такая.

Compare:

• такой вопрос — such a question (masculine)
• такая проблема — such a problem (feminine)
• такое решение — such a solution/decision (neuter)
• такие проблемы — such problems (plural)

It is in the nominative singular.

That is because проблема is the subject of the sentence — it is the thing that exists.

So:

• такая проблема = the subject
• существует = the verb

Both такая and проблема are nominative because they belong to the subject phrase.

Существует is the 3rd person singular present tense form of существовать.

So:

• существовать — to exist
• существует — exists

It matches проблема, which is singular:

• Проблема существует — The problem exists

If the subject were plural, you would use:

• Такие проблемы существуют — Such problems exist

Because Russian does not normally use the present-tense copula to be the way English does.

Also, in this sentence the main verb is already существует = exists, so nothing else is needed.

English:

• Such a problem exists

Russian:

• Такая проблема существует

You do not need a separate word for is here.

Not exactly.

• есть often means there is / there are
• существует means exists

So существует sounds a bit more explicit and often a bit more formal or abstract. It emphasizes actual existence.

Compare:

• Такая проблема есть — There is such a problem (more conversational, context-dependent)
• Такая проблема существует — Such a problem exists (more explicit, often more neutral/formal)

In many contexts both can work, but существует is the clearer choice when you want to stress that something really does exist.

Yes. Russian word order is flexible.

You can say:

• Такая проблема существует
• Существует такая проблема

Both are correct, but the emphasis is slightly different.

A rough idea of the difference:

• Существует такая проблема — often sounds like introducing the fact: There is such a problem
• Такая проблема существует — can sound a little more like confirming or emphasizing the problem itself: Such a problem does exist

In real usage, both are natural.

It sounds fairly neutral, but существует can make it feel a little more formal, written, or analytical than everyday casual speech.

You might hear it in:

• explanations
• articles
• presentations
• discussions of social, technical, or abstract issues

In casual speech, people may also say things like:

• Есть такая проблема
• Такая проблема есть

Those can sound more conversational.

Yes, but the meaning changes.

• Такая проблема существует — Such a problem exists / This kind of problem exists
• Проблема существует — The problem exists / A problem exists

So такая is important if you want to refer to a particular type of problem or connect back to something already mentioned.

The stress is:

• така́я
• пробле́ма
• существу́ет

So the full sentence is:

така́я пробле́ма существу́ет

A rough English-style pronunciation guide:

ta-KA-ya pra-BLYE-ma soo-shchest-VOO-yet

A few notes:

• я in такая is pronounced like ya
• щ in существует is a soft shch sound
• unstressed o is reduced in pronunciation, so проблема does not sound exactly like written pro-

Not always exactly. Такой / такая / такое / такие can mean slightly different things depending on context:

• such
• this kind of
• like that
• so ... in some patterns

In this sentence, the most natural sense is such a or this kind of.

So the phrase is not just naming a problem; it is classifying it as a certain kind of problem.