Entire Blow-Up Solutions of Semilinear Elliptic Equations and Systems
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We examine two problems concerning semilinear elliptic equations. We also give alternative conditions that ensure existence of nonnegative radial solutions blowing up at infinity. Similarly, for systems, we provide conditions on p, q, f and g that guarantee existence of nonnegative solutions on the entire space. In this case, the main requirement for f and g will be closely related to a growth requirement known as the Keller-Osserman condition. Further, we demonstrate the existence of solutions blowing up at infinity and describe a setof initial conditionsthat would generate such solutions. La...
We examine two problems concerning semilinear elliptic equations. We also give alternative conditions that ensure existence of nonnegative radial solutions blowing up at infinity. Similarly, for systems, we provide conditions on p, q, f and g that guarantee existence of nonnegative solutions on the entire space. In this case, the main requirement for f and g will be closely related to a growth requirement known as the Keller-Osserman condition. Further, we demonstrate the existence of solutions blowing up at infinity and describe a setof initial conditionsthat would generate such solutions. Lastly, we examine several specific equations and systems numerically to graphically demonstrate the results of our analysis. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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