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Positive solutions to a nonlinear abel-type integral equation on the whole line
Affiliation:Institute of Mathematics, Technical University of Wroca̵w Wybrzeze Wyspiańskiego 27, 50-370 Wroca̵w, Poland;Institute of Mathematics, Technical University of Zielona Góra ul.Podgórna 50, 65-246 Zielona Góra, Poland
Abstract:We consider the existence of positive solutions to the nonlinear integral equation
></figure> where <em>g</em> is a continuous, nondecreasing function such that <em>g</em>(0) = 0. We show that the equation always has nontrivial solutions and we give a necessary and sufficient condition for the existence of solutions <em>u</em> such that <em>u</em>(<em>x</em>) > − ∞. We also provide a condition which ensures that all the nontrivial solutions experience the blow-up behaviour.</td>
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