Take a look at the Mojo::DOM documentation; especially the part regarding the at method, whose first sentence is:

"Find first descendant element of this element matching the CSS selector and return it as a Mojo::DOM object, or undef if none could be found."

Your posted error message reflects what the documentation describes; i.e. $dom1->at('div.abstract-content > p') is returning undef. I can reproduce this:

$ perl -MMojo::DOM -E 'my $dom = Mojo::DOM::->new("<p></p>"); my $x = 
+$dom->at("p.missing")->text(); say defined $x ? "not missing" : "real
+ly missing"'
Can't call method "text" on an undefined value at -e line 1.
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In order to "catch the exception", you should get the return value from $dom1->at('div.abstract-content > p'). If it is defined, you can use it to invoke the text() method; otherwise, handle as appropriate for your application (output a warning, write to a log, etc.). Based on my code above, you'd want something like this:

$ perl -MMojo::DOM -E 'my $dom = Mojo::DOM::->new("<p></p>"); my $x = 
+$dom->at("p.missing"); say defined $x ? "not missing" : "really missi
+ng"'
really missing
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Update (additional example): Something of an afterthought and really just intended to show the validity of the previous example:

$ perl -MMojo::DOM -E 'my $dom = Mojo::DOM::->new(q{<p class="missing"
+></p>"}); my $x = $dom->at("p.missing"); say defined $x ? "not missin
+g" : "really missing"'
not missing
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